Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
330 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 330 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. #26012542 | C2 | semidirect |
| 2. #26012541 | C2 | semidirect |
| 3. #26012540 | C2 | semidirect |
| 4. Q8×#13063443 | C2 | semidirect |
| 87. C173 | #2986 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012542 | 2 |
| #26012541 | 2 |
| #26012540 | 2 |
| Q8×#13063443 | 2 |
| #26012516 | 2 |
| #26012510 | 2 |
| #26012046 | 2 |
| #2986 | 173 |