Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
344 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 79 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. #26012257 | C2 | semidirect |
| 3. #26011497 | C2 | semidirect |
| 4. #26011495 | C2 | semidirect |
| 5. #26011464 | C2 | semidirect |
| 6. #26011247 | C2 | semidirect |
| 7. H(3,ℤ/4)×C173 | C2 | semidirect |
| 14. #19149676 | C4 | semidirect |
| 15. #19149667 | C4 | semidirect |
| 44. C2×#13063436 | D4 | semidirect |
| 53. C2×C8×C173 | D4 | semidirect |
| 115. C173 | #1910 | semidirect |
| 123. H(3,ℤ/4) | D173 | semidirect |
| 165. C2×C8 | D692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012257 | 2 |
| #26012060 | 2 |
| #26011497 | 2 |
| #26011495 | 2 |
| #26011464 | 2 |
| #26011247 | 2 |
| H(3,ℤ/4)×C173 | 2 |
| #1910 | 173 |