Finite Group DatabasebetaFinite Group DatabasebetaOrder 22912.
216 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 216 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. #26038879 | C2 | semidirect |
| 2. C2×#19153057 | C2 | semidirect |
| 3. #26038714 | C2 | semidirect |
| 4. #26038252 | C2 | semidirect |
| 5. #26038246 | C2 | semidirect |
| 6. #26038223 | C2 | semidirect |
| 9. C2×Dic716 | C22 | semidirect |
| 13. #19153053 | C22 | semidirect |
| 14. C2×C179⋊C16 | C22 | semidirect |
| 15. #19153049 | C22 | semidirect |
| 91. C179 | #2194 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26038879 | 2 |
| C2×#19153057 | 2 |
| #26038714 | 2 |
| #26038252 | 2 |
| #26038246 | 2 |
| #26038223 | 2 |
| #576×C179 | 2 |
| #2194 | 179 |