Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
13310 conjugacy classes of subgroups; only the 6264 normal subgroups are shown.
This group has 13310 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. C23×#63243 | C2 | direct (N × H) |
| 2. C24×#3624 | C2 | semidirect |
| 4. C22×#63243 | C22 | direct (N × H) |
| 5. C23×#3624 | C22 | semidirect |
| 19. C22×#3624 | C23 | semidirect |
| 20. C2×#63243 | C23 | direct (N × H) |
| 21. C24×C17 | M16 | semidirect |
| 30. C2×#3624 | C24 | semidirect |
| 31. #63243 | C24 | direct (N × H) |
| 33. C23×C17 | C2×M16 | semidirect |
| 42. #3624 | C25 | semidirect |
| 46. C22×C17 | C22×M16 | semidirect |
| 60. C2×C17 | C23×M16 | semidirect |
| 73. C17 | C24×M16 | semidirect |
| 76. C24 | #63243 | direct (N × H) |
| 87. C23 | C2×#63243 | direct (N × H) |
| 97. C22 | C22×#63243 | direct (N × H) |
| 103. C2 | C23×#63243 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#63243 | 2 |
| C24×#3624 | 2 |
| C24×C4×D17 | 2 |
| C24×M16 | 17 |