Finite Group DatabasebetaFinite Group DatabasebetaOrder 26944.
120 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 41 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. C2×#20269758 | C2 | semidirect |
| 2. C2×#20269755 | C2 | semidirect |
| 4. #27212299 | C2 | semidirect |
| 5. #27212290 | C2 | semidirect |
| 6. #27212286 | C2 | semidirect |
| 7. C22⋊Q8×C421 | C2 | semidirect |
| 27. #16809890 | D4 | semidirect |
| 55. C421 | #468 | semidirect |
| 59. C22⋊Q8 | D421 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20269758 | 2 |
| C2×#20269755 | 2 |
| #27212340 | 2 |
| #27212299 | 2 |
| #27212290 | 2 |
| #27212286 | 2 |
| C22⋊Q8×C421 | 2 |
| #468 | 421 |