Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
380 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 380 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 |
|---|---|---|
| 1. #26012289 | C2 | semidirect |
| 2. C2×#19149704 | C2 | semidirect |
| 3. #26012060 | C2 | semidirect |
| 4. #26011509 | C2 | semidirect |
| 5. #26011495 | C2 | semidirect |
| 6. #26011261 | C2 | semidirect |
| 7. #410×C173 | C2 | semidirect |
| 56. #14583810 | D4 | semidirect |
| 58. C2×#13063436 | D4 | semidirect |
| 64. C2×Q8×C173 | D4 | semidirect |
| 66. C2×D4×C173 | D4 | semidirect |
| 142. C173 | #2008 | semidirect |
| 149. #410 | D173 | semidirect |
| 184. C2×Q8 | D692 | semidirect |
| 195. C2×D4 | D692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012289 | 2 |
| C2×#19149704 | 2 |
| #26012060 | 2 |
| #26011509 | 2 |
| #26011495 | 2 |
| #26011261 | 2 |
| #410×C173 | 2 |
| #2008 | 173 |