Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
12446 conjugacy classes of subgroups; only the 6264 normal subgroups are shown.
This group has 12446 conjugacy classes of subgroups — too many to draw. Only its 6264 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×Q8×#595 | C2 | direct (N × H) |
| 7. C2×Q8×#595 | C22 | direct (N × H) |
| 10. C23×Dic34 | C4 | semidirect |
| 11. C22×Q8×D17 | C4 | semidirect |
| 14. C23×Q8×C17 | C4 | semidirect |
| 17. C23×#595 | Q8 | direct (N × H) |
| 20. C22×Q8×C17 | C2×C4 | semidirect |
| 23. C2×Q8×D17 | C2×C4 | semidirect |
| 27. C22×Dic34 | C2×C4 | semidirect |
| 28. Q8×#595 | C23 | direct (N × H) |
| 37. C22×#595 | C2×Q8 | direct (N × H) |
| 40. C2×Q8×C17 | C22×C4 | semidirect |
| 43. Q8×D17 | C22×C4 | semidirect |
| 47. C2×Dic34 | C22×C4 | semidirect |
| 51. C23×C17 | C4×Q8 | semidirect |
| 53. C22×D17 | C4×Q8 | semidirect |
| 59. C2×#595 | C22×Q8 | direct (N × H) |
| 62. Q8×C17 | C23×C4 | semidirect |
| 67. Dic34 | C23×C4 | semidirect |
| 72. C22×C17 | C2×C4×Q8 | semidirect |
| 74. C2×D17 | C2×C4×Q8 | semidirect |
| 80. #595 | C23×Q8 | direct (N × H) |
| 86. C23×Q8 | #595 | direct (N × H) |
| 93. C2×C17 | C22×C4×Q8 | semidirect |
| 95. D17 | C22×C4×Q8 | semidirect |
| 102. C22×Q8 | C2×#595 | direct (N × H) |
| 114. C17 | C23×C4×Q8 | semidirect |
| 123. C2×Q8 | C22×#595 | direct (N × H) |
| 139. C23 | Q8×#595 | direct (N × H) |
| 142. Q8 | C23×#595 | direct (N × H) |
| 156. C22 | C2×Q8×#595 | direct (N × H) |
| 165. C2 | C22×Q8×#595 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×#595 | 2 |
| C23×C4⋊#595 | 2 |
| C23×C4×#595 | 2 |
| C23×Q8×D17 | 2 |
| C23×C4×Q8 | 17 |