Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
162 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 54 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. #26012541 | C2 | semidirect |
| 3. #26012355 | C2 | semidirect |
| 4. #26012341 | C2 | semidirect |
| 6. #26012332 | C2 | semidirect |
| 54. #13063436 | M16 | semidirect |
| 77. C173 | #1592 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012541 | 2 |
| #26012526 | 2 |
| #26012355 | 2 |
| #26012341 | 2 |
| D4⋊#13063443 | 2 |
| #26012332 | 2 |
| #26011582 | 2 |
| #1592 | 173 |