Finite Group DatabasebetaFinite Group DatabasebetaOrder 22912.
198 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 53 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. #26038815 | C2 | semidirect |
| 2. #26038634 | C2 | semidirect |
| 3. #26038517 | C2 | semidirect |
| 4. #26038189 | C2 | semidirect |
| 5. #26038183 | C2 | semidirect |
| 6. #26038182 | C2 | semidirect |
| 7. #459×C179 | C2 | semidirect |
| 53. C179⋊C8 | D8 | semidirect |
| 92. C179 | #1687 | semidirect |
| 96. #459 | D179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26038815 | 2 |
| #26038634 | 2 |
| #26038517 | 2 |
| #26038189 | 2 |
| #26038183 | 2 |
| #26038182 | 2 |
| #459×C179 | 2 |
| #1687 | 179 |