Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
14334 conjugacy classes of subgroups; only the 7902 normal subgroups are shown.
This group has 14334 conjugacy classes of subgroups — too many to draw. Only its 7902 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×C67 | C22 |
| commutator | C2 | C23×C42×C67 |
| Frattini, cosocle | C23 | C25×C67 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C26×C67 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×#95×C67 | C2 | direct (N × H) |
| 5. C24×C4×C67 | C4 | semidirect |
| 7. C2×#95×C67 | C22 | direct (N × H) |
| 14. C23×C4×C67 | C2×C4 | semidirect |
| 16. #95×C67 | C23 | direct (N × H) |
| 26. C22×C4×C67 | C22×C4 | semidirect |
| 28. C23×C67 | #95 | direct (N × H) |
| 38. C2×C4×C67 | C23×C4 | semidirect |
| 39. C22×C67 | C2×#95 | direct (N × H) |
| 47. C23×#95 | C67 | direct (N × H) |
| 48. C2×C67 | C22×#95 | direct (N × H) |
| 53. C22×#95 | C2×C67 | direct (N × H) |
| 54. C67 | C23×#95 | direct (N × H) |
| 57. C24×C4 | C4×C67 | semidirect |
| 59. C2×#95 | C22×C67 | direct (N × H) |
| 66. C23×C4 | C2×C4×C67 | semidirect |
| 68. #95 | C23×C67 | direct (N × H) |
| 78. C22×C4 | C22×C4×C67 | semidirect |
| 80. C23 | #95×C67 | direct (N × H) |
| 90. C2×C4 | C23×C4×C67 | semidirect |
| 91. C22 | C2×#95×C67 | direct (N × H) |
| 99. C2 | C22×#95×C67 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×C4×C67 | 2 |
| C22×#95×C67 | 2 |
| C23×#95 | 67 |