Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
2598 conjugacy classes of subgroups; only the 1374 normal subgroups are shown.
This group has 2598 conjugacy classes of subgroups — too many to draw. Only its 1374 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C67 | C24 |
| commutator | C2 | C2×C43×C67 |
| Frattini, cosocle | C24 | C24×C67 |
| prime radical | C25×C67 | C23 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24×C67 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C4×#95×C67 | C2 | semidirect |
| 7. C4×C22⋊C4×C67 | C4 | semidirect |
| 8. C2×#95×C67 | C4 | semidirect |
| 19. C2×C42×C67 | C2×C4 | semidirect |
| 21. #95×C67 | C2×C4 | semidirect |
| 32. C22×C4×C67 | C42 | semidirect |
| 37. C22⋊C4×C67 | C42 | semidirect |
| 69. #13749 | C67 | direct (N × H) |
| 77. C4×#95 | C2×C67 | semidirect |
| 78. C67 | #13749 | direct (N × H) |
| 82. C4×C22⋊C4 | C4×C67 | semidirect |
| 83. C2×#95 | C4×C67 | semidirect |
| 94. C2×C42 | C2×C4×C67 | semidirect |
| 96. #95 | C2×C4×C67 | semidirect |
| 107. C22×C4 | C42×C67 | semidirect |
| 112. C22⋊C4 | C42×C67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C22⋊C4×C67 | 2 |
| C22×#95×C67 | 2 |
| C4×#95×C67 | 2 |
| #13749 | 67 |