Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
346 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 66 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. #26012489 | C2 | semidirect |
| 3. #26012483 | C2 | semidirect |
| 4. #26012471 | C2 | semidirect |
| 5. #26012373 | C2 | semidirect |
| 6. #26012359 | C2 | semidirect |
| 22. C2×#14583815 | C4 | semidirect |
| 23. C2×#14583814 | C4 | semidirect |
| 24. C2×#14583811 | C4 | semidirect |
| 26. C2×D8×C173 | C4 | semidirect |
| 46. C2×Dic346 | C2×C4 | semidirect |
| 61. C2×#13063436 | C2×C4 | semidirect |
| 63. C2×D4×C173 | C2×C4 | semidirect |
| 65. C2×C8×C173 | C2×C4 | semidirect |
| 128. C173 | #1904 | semidirect |
| 144. C2×D8 | #10621924 | semidirect |
| 170. C2×D4 | C2×#10621924 | semidirect |
| 184. C2×C8 | C2×#10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012558 | 2 |
| #26012489 | 2 |
| #26012483 | 2 |
| #26012471 | 2 |
| #26012373 | 2 |
| #26012359 | 2 |
| C2×#19149703 | 2 |
| #1904 | 173 |