Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
380 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 89 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. #14545978 | C2 | semidirect |
| 2. #14545893 | C2 | semidirect |
| 3. #14545837 | C2 | semidirect |
| 8. #11763913 | C22 | semidirect |
| 9. #11763893 | C22 | semidirect |
| 36. C2×Q16×C17 | C8 | semidirect |
| 40. #10587605 | C8 | semidirect |
| 42. C2×D136 | C8 | semidirect |
| 165. C2×Q16 | #3633 | semidirect |
| 192. C17 | #11604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545978 | 2 |
| #14545893 | 2 |
| #14545837 | 2 |
| C2×#11763853 | 2 |
| #11604 | 17 |