Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
696 conjugacy classes of subgroups; only the 234 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 234 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. #14544883 | C2 | semidirect |
| 3. #14544838 | C2 | semidirect |
| 5. #14544716 | C2 | semidirect |
| 6. #14544711 | C2 | semidirect |
| 39. #10587562 | C8 | semidirect |
| 66. C42×C17 | C2×C8 | semidirect |
| 70. #63225 | C2×C8 | semidirect |
| 167. C17 | #23375 | semidirect |
| 194. C42 | #63242 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544883 | 2 |
| #14544856 | 2 |
| #14544838 | 2 |
| #14544729 | 2 |
| #14544716 | 2 |
| #14544711 | 2 |
| #14531332 | 2 |
| #23375 | 17 |