Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
284 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 284 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. #26012501 | C2 | semidirect |
| 2. #26012490 | C2 | semidirect |
| 3. #26012489 | C2 | semidirect |
| 4. #26012472 | C2 | semidirect |
| 5. #26012471 | C2 | semidirect |
| 6. #26012454 | C2 | semidirect |
| 26. C2×#14583816 | C4 | semidirect |
| 27. C2×#14583815 | C4 | semidirect |
| 28. C2×#14583811 | C4 | semidirect |
| 30. C2×SD16×C173 | C4 | semidirect |
| 132. C173 | #1976 | semidirect |
| 149. C2×SD16 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012501 | 2 |
| #26012490 | 2 |
| #26012489 | 2 |
| #26012472 | 2 |
| #26012471 | 2 |
| #26012454 | 2 |
| C2×#19149700 | 2 |
| #1976 | 173 |