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. #26012472 | C2 | semidirect |
| 4. #26012454 | C2 | semidirect |
| 20. C2×#14583813 | C4 | semidirect |
| 21. C2×D1384 | C4 | semidirect |
| 23. C2×Q16×C173 | C4 | semidirect |
| 96. C173 | #1976 | semidirect |
| 108. C2×Q16 | #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 |
| #26012472 | 2 |
| #26012454 | 2 |
| C2×#19149702 | 2 |
| #1976 | 173 |