Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
224 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 2. #14527682 | C2 | semidirect |
| 4. #14526858 | C2 | semidirect |
| 5. #14526749 | C2 | semidirect |
| 7. C8×C16×C17 | C2 | semidirect |
| 67. C16×C17 | M16 | semidirect |
| 85. C8×C17 | SD32 | semidirect |
| 96. C8×C16 | D17 | semidirect |
| 149. C17 | #12082 | semidirect |
| 173. C16 | #63218 | semidirect |
| 192. C8 | #10587471 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#10587471 | 2 |
| #14527682 | 2 |
| #14527670 | 2 |
| #14526858 | 2 |
| #14526749 | 2 |
| #14526746 | 2 |
| C8×C16×C17 | 2 |
| #12082 | 17 |