Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
362 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 362 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 |
|---|---|---|
| 2. #26011965 | C2 | semidirect |
| 3. #26011509 | C2 | semidirect |
| 4. #26011507 | C2 | semidirect |
| 5. C2×#19149595 | C2 | semidirect |
| 6. #26011247 | C2 | semidirect |
| 7. H(3,ℤ/4)×C173 | C2 | semidirect |
| 11. #19149676 | C4 | semidirect |
| 12. #19149667 | C4 | semidirect |
| 30. C2×Dic346 | C2×C4 | semidirect |
| 37. C2×D692 | C2×C4 | semidirect |
| 49. C4×Dic173 | D4 | semidirect |
| 58. C42×C173 | C2×C4 | semidirect |
| 59. C42×C173 | D4 | semidirect |
| 116. C173 | #1911 | semidirect |
| 124. H(3,ℤ/4) | D173 | semidirect |
| 175. C42 | C4×D173 | semidirect |
| 176. C42 | D692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012060 | 2 |
| #26011965 | 2 |
| #26011509 | 2 |
| #26011507 | 2 |
| C2×#19149595 | 2 |
| #26011247 | 2 |
| H(3,ℤ/4)×C173 | 2 |
| #1911 | 173 |