Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
402 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 122 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. #14544990 | C2 | semidirect |
| 2. C2×#11763670 | C2 | semidirect |
| 3. #14543744 | C2 | semidirect |
| 4. #14543742 | C2 | semidirect |
| 26. C17×#135 | C8 | semidirect |
| 71. Q16×C17 | C2×C8 | semidirect |
| 74. D8×C17 | C2×C8 | semidirect |
| 173. #135 | #3624 | semidirect |
| 205. C17 | #11598 | semidirect |
| 218. Q16 | C2×#3624 | semidirect |
| 221. D8 | C2×#3624 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544990 | 2 |
| C2×#11763670 | 2 |
| #14543744 | 2 |
| #14543742 | 2 |
| #135×Dic17 | 2 |
| #11598 | 17 |