Finite Group DatabasebetaFinite Group DatabasebetaOrder 26944.
124 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 48 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×#20269781 | C2 | semidirect |
| 2. C22×#16809897 | C2 | semidirect |
| 3. C4⋊#16809897 | C2 | semidirect |
| 4. #27212423 | C2 | semidirect |
| 5. C22⋊#16809897 | C2 | semidirect |
| 6. #27212421 | C2 | semidirect |
| 24. #16809897 | D4 | semidirect |
| 39. C22×C421 | M16 | semidirect |
| 55. C421 | #435 | semidirect |
| 98. C22 | #20269781 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20269781 | 2 |
| C22×#16809897 | 2 |
| C4⋊#16809897 | 2 |
| #27212423 | 2 |
| C22⋊#16809897 | 2 |
| #27212421 | 2 |
| #27212326 | 2 |
| #435 | 421 |