Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
240 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 68 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. #14544416 | C2 | semidirect |
| 2. D8×#3624 | C2 | semidirect |
| 3. #14543815 | C2 | semidirect |
| 4. #14543739 | C2 | semidirect |
| 5. #14543738 | C2 | semidirect |
| 6. #14543698 | C2 | semidirect |
| 56. D8×C17 | M16 | semidirect |
| 89. #3624 | D16 | semidirect |
| 155. C17 | #12069 | semidirect |
| 163. D8 | #63243 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544416 | 2 |
| D8×#3624 | 2 |
| #14543815 | 2 |
| #14543739 | 2 |
| #14543738 | 2 |
| #14543698 | 2 |
| #14530628 | 2 |
| #12069 | 17 |