Finite Group DatabasebetaFinite Group DatabasebetaOrder 22912.
316 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 316 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. C2×#19153048 | C2 | semidirect |
| 3. #26038445 | C2 | semidirect |
| 4. #26038444 | C2 | semidirect |
| 5. C2×#19153029 | C2 | semidirect |
| 6. #26038397 | C2 | semidirect |
| 7. C2×#100×C179 | C2 | semidirect |
| 12. C2×#15668244 | C4 | semidirect |
| 111. C179 | #1978 | semidirect |
| 118. C2×#100 | D179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668244 | 2 |
| C2×#19153048 | 2 |
| #26038445 | 2 |
| #26038444 | 2 |
| C2×#19153029 | 2 |
| #26038397 | 2 |
| C2×#100×C179 | 2 |
| #1978 | 179 |