Finite Group DatabasebetaFinite Group DatabasebetaOrder 22912.
256 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 61 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. C2×#19153057 | C2 | semidirect |
| 2. #26038680 | C2 | semidirect |
| 3. #26038240 | C2 | semidirect |
| 4. C22⋊(C179⋊C16) | C2 | semidirect |
| 6. C2×Dic716 | C22 | semidirect |
| 9. C2×C179⋊C16 | C22 | semidirect |
| 10. #19153047 | C22 | semidirect |
| 59. C22×C179 | SD32 | semidirect |
| 71. C179 | #2187 | semidirect |
| 131. C22 | #19153057 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153057 | 2 |
| #26038680 | 2 |
| #26038240 | 2 |
| C22⋊(C179⋊C16) | 2 |
| C22×D8×C179 | 2 |
| #2187 | 179 |