Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
19742 conjugacy classes of subgroups; only the 15454 normal subgroups are shown.
This group has 19742 conjugacy classes of subgroups — too many to draw. Only its 15454 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C26×C23 | C22 |
| commutator | C2 | C25×C4×C23 |
| Frattini, cosocle | C22 | C26×C23 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C26×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C23×C4⋊C4×C23 | C2 | direct (N × H) |
| 6. C24×C4×C23 | C4 | semidirect |
| 9. C22×C4⋊C4×C23 | C22 | direct (N × H) |
| 15. C23×C4×C23 | C2×C4 | semidirect |
| 18. C2×C4⋊C4×C23 | C23 | direct (N × H) |
| 19. C24×C23 | C4⋊C4 | direct (N × H) |
| 25. C22×C4×C23 | C22×C4 | semidirect |
| 28. C4⋊C4×C23 | C24 | direct (N × H) |
| 29. C24×C4⋊C4 | C23 | direct (N × H) |
| 30. C23×C23 | C2×C4⋊C4 | direct (N × H) |
| 36. C2×C4×C23 | C23×C4 | semidirect |
| 41. C23×C4⋊C4 | C2×C23 | direct (N × H) |
| 42. C22×C23 | C22×C4⋊C4 | direct (N × H) |
| 48. C4×C23 | C24×C4 | semidirect |
| 51. C24×C4 | C4×C23 | semidirect |
| 54. C22×C4⋊C4 | C22×C23 | direct (N × H) |
| 55. C2×C23 | C23×C4⋊C4 | direct (N × H) |
| 64. C23×C4 | C2×C4×C23 | semidirect |
| 67. C2×C4⋊C4 | C23×C23 | direct (N × H) |
| 68. C23 | C24×C4⋊C4 | direct (N × H) |
| 69. C24 | C4⋊C4×C23 | direct (N × H) |
| 75. C22×C4 | C22×C4×C23 | semidirect |
| 78. C4⋊C4 | C24×C23 | direct (N × H) |
| 79. C23 | C2×C4⋊C4×C23 | direct (N × H) |
| 85. C2×C4 | C23×C4×C23 | semidirect |
| 88. C22 | C22×C4⋊C4×C23 | direct (N × H) |
| 94. C4 | C24×C4×C23 | semidirect |
| 95. C2 | C23×C4⋊C4×C23 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×C4×C23 | 2 |
| C23×C4⋊C4×C23 | 2 |
| C24×C4⋊C4 | 23 |