Finite Group DatabasebetaFinite Group DatabasebetaOrder 22912.
156 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 4. #26038266 | C2 | semidirect |
| 5. #26038265 | C2 | semidirect |
| 6. #26038264 | C2 | semidirect |
| 7. #367×C179 | C2 | semidirect |
| 11. #19153052 | C4 | semidirect |
| 30. C179⋊C16 | C2×C4 | semidirect |
| 34. C16×C179 | C2×C4 | semidirect |
| 63. C179 | #2159 | semidirect |
| 69. #367 | D179 | semidirect |
| 98. C16 | C4×D179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153052 | 2 |
| #26038476 | 2 |
| #107×D179 | 2 |
| #26038266 | 2 |
| #26038265 | 2 |
| #26038264 | 2 |
| #367×C179 | 2 |
| #2159 | 179 |