Finite Group DatabasebetaFinite Group DatabasebetaOrder 22912.
346 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 85 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. #26038914 | C2 | semidirect |
| 3. #26038455 | C2 | semidirect |
| 4. #26038412 | C2 | semidirect |
| 5. #26038211 | C2 | semidirect |
| 6. #26038195 | C2 | semidirect |
| 7. #418×C179 | C2 | semidirect |
| 11. C2×#15668247 | C4 | semidirect |
| 12. C2×#15668244 | C4 | semidirect |
| 29. C2×Dic358 | C2×C4 | semidirect |
| 30. C2×D716 | C2×C4 | semidirect |
| 38. C2×C179⋊C8 | C2×C4 | semidirect |
| 115. C179 | #1904 | semidirect |
| 120. #418 | D179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153139 | 2 |
| #26038914 | 2 |
| #26038455 | 2 |
| #26038412 | 2 |
| #26038211 | 2 |
| #26038195 | 2 |
| #418×C179 | 2 |
| #1904 | 179 |