Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
236 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 61 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. #26011865 | C2 | semidirect |
| 2. #26011691 | C2 | semidirect |
| 4. #26011240 | C2 | semidirect |
| 5. Q8⋊#13063436 | C2 | semidirect |
| 6. D4⋊#13063436 | C2 | semidirect |
| 7. #554×C173 | C2 | semidirect |
| 64. D4×C173 | SD16 | semidirect |
| 96. C173 | #1622 | semidirect |
| 98. #554 | D173 | semidirect |
| 158. D4 | #14583813 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011865 | 2 |
| #26011691 | 2 |
| #26011686 | 2 |
| #26011240 | 2 |
| Q8⋊#13063436 | 2 |
| D4⋊#13063436 | 2 |
| #554×C173 | 2 |
| #1622 | 173 |