Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
410 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 152 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. #26012526 | C2 | semidirect |
| 2. D4×#13063443 | C2 | semidirect |
| 3. #26012510 | C2 | semidirect |
| 4. #26012464 | C2 | semidirect |
| 71. C173 | #2979 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012526 | 2 |
| D4×#13063443 | 2 |
| #26012510 | 2 |
| #26012464 | 2 |
| #26012039 | 2 |
| #2979 | 173 |