Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
492 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 3. #26021972 | C2 | semidirect |
| 5. #26018360 | C2 | semidirect |
| 6. #26018348 | C2 | semidirect |
| 7. C2×#358×C89 | C2 | semidirect |
| 13. #19151870 | C4 | semidirect |
| 51. #15667948 | C2×C4 | semidirect |
| 64. C2×Q16×C89 | C2×C4 | semidirect |
| 185. C2×#358 | D89 | semidirect |
| 189. C89 | #12997 | semidirect |
| 220. C2×Q16 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151870 | 2 |
| #26028848 | 2 |
| #26021972 | 2 |
| C2×#19151381 | 2 |
| #26018360 | 2 |
| #26018348 | 2 |
| C2×#358×C89 | 2 |
| #12997 | 89 |