Finite Group DatabasebetaFinite Group DatabasebetaOrder 22912.
160 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 51 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. #26038843 | C2 | semidirect |
| 3. #26038241 | C2 | semidirect |
| 4. #26038240 | C2 | semidirect |
| 5. #26038239 | C2 | semidirect |
| 6. C16×Dic179 | C2 | semidirect |
| 7. #357×C179 | C2 | semidirect |
| 72. C179 | #2240 | semidirect |
| 79. #357 | D179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26038843 | 2 |
| #26038814 | 2 |
| #26038241 | 2 |
| #26038240 | 2 |
| #26038239 | 2 |
| C16×Dic179 | 2 |
| #357×C179 | 2 |
| #2240 | 179 |