Finite Group DatabasebetaFinite Group DatabasebetaOrder 22912.
272 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 109 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. C22×C179⋊C16 | C2 | semidirect |
| 2. C2×#19153047 | C2 | semidirect |
| 3. #26038240 | C2 | direct (N × H) |
| 7. C2×C179⋊C16 | C22 | semidirect |
| 9. #19153047 | C22 | semidirect |
| 13. C2×D8×C179 | C4 | semidirect |
| 28. D8×C179 | C2×C4 | semidirect |
| 63. C2×C179 | #357 | semidirect |
| 67. C179 | C2×#357 | semidirect |
| 76. C2×D8 | Dic179 | semidirect |
| 93. D8 | C2×Dic179 | semidirect |
| 131. C2 | #26038240 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C179⋊C16 | 2 |
| C2×#19153047 | 2 |
| #26038240 | 2 |
| C22×D8×C179 | 2 |
| C2×#357 | 179 |