Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
384 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 154 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. #26012515 | C2 | semidirect |
| 2. #26012512 | C2 | semidirect |
| 3. #26012511 | C2 | semidirect |
| 4. #26012498 | C2 | semidirect |
| 6. C4×#14583836 | C2 | semidirect |
| 7. #26012450 | C2 | semidirect |
| 104. C173 | #2923 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012515 | 2 |
| #26012512 | 2 |
| #26012511 | 2 |
| #26012498 | 2 |
| #26012465 | 2 |
| C4×#14583836 | 2 |
| #26012450 | 2 |
| C4×#14583825 | 2 |
| #2923 | 173 |