Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
562 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 562 conjugacy classes of subgroups — too many to draw. Only its 165 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. #14541759 | C2 | semidirect |
| 2. Q8×D136 | C2 | semidirect |
| 3. #14531008 | C2 | semidirect |
| 4. #14530922 | C2 | semidirect |
| 5. #14530820 | C2 | semidirect |
| 6. C4×D272 | C2 | semidirect |
| 7. Q8×C16×C17 | C2 | semidirect |
| 69. D136 | #41 | semidirect |
| 75. Q8×C17 | D16 | semidirect |
| 98. Q8×C16 | D17 | semidirect |
| 156. C17 | #33925 | semidirect |
| 186. Q8 | D272 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14541759 | 2 |
| Q8×D136 | 2 |
| #14531008 | 2 |
| #14530922 | 2 |
| #14530820 | 2 |
| C4×D272 | 2 |
| Q8×C16×C17 | 2 |
| #33925 | 17 |