Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
578 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 68 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. #26012558 | C2 | semidirect |
| 2. D173⋊#99 | C2 | semidirect |
| 3. #26012432 | C2 | semidirect |
| 4. #26012368 | C2 | semidirect |
| 18. #19149649 | C4 | semidirect |
| 19. #19149648 | C4 | semidirect |
| 21. #19149647 | C4 | semidirect |
| 24. #120×C173 | C4 | semidirect |
| 27. C22×#10621924 | D4 | semidirect |
| 41. C23×D173 | C2×C4 | semidirect |
| 56. C22⋊Dic173 | C2×C4 | semidirect |
| 60. C24×C173 | C2×C4 | semidirect |
| 64. C22⋊C4×C173 | C2×C4 | semidirect |
| 88. C22×D173 | C22⋊C4 | semidirect |
| 100. C2×Dic173 | C22⋊C4 | semidirect |
| 107. C23×C173 | C22⋊C4 | semidirect |
| 112. C2×C4×C173 | C22⋊C4 | semidirect |
| 158. C173 | #1889 | semidirect |
| 173. #120 | #10621924 | semidirect |
| 192. C24 | C2×#10621924 | semidirect |
| 222. C22⋊C4 | C2×#10621924 | semidirect |
| 250. C23 | C22⋊#10621924 | semidirect |
| 271. C2×C4 | C22⋊#10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012558 | 2 |
| D173⋊#99 | 2 |
| #26012432 | 2 |
| #26012368 | 2 |
| #120×D173 | 2 |
| #1889 | 173 |