Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
406 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 168 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. #26012542 | C2 | semidirect |
| 2. #26012522 | C2 | semidirect |
| 3. D4×#13063443 | C2 | semidirect |
| 4. #26012512 | C2 | semidirect |
| 5. #26012511 | C2 | semidirect |
| 6. C4×#14583835 | C2 | semidirect |
| 7. C2×#19149734 | C2 | semidirect |
| 62. #13063443 | #41 | semidirect |
| 77. D4×C173 | M16 | semidirect |
| 104. C173 | #2970 | semidirect |
| 169. D4 | #14583835 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012542 | 2 |
| #26012522 | 2 |
| D4×#13063443 | 2 |
| #26012512 | 2 |
| #26012511 | 2 |
| C4×#14583835 | 2 |
| C2×#19149734 | 2 |
| #41×Dic173 | 2 |
| #2970 | 173 |