Finite Group DatabasebetaFinite Group DatabasebetaOrder 26944.
152 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 39 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 |
|---|---|---|
| 2. #27212399 | C2 | semidirect |
| 3. #27212396 | C2 | semidirect |
| 4. #27212354 | C2 | semidirect |
| 5. #27212294 | C2 | semidirect |
| 6. #27212282 | C2 | semidirect |
| 7. #104×C421 | C2 | semidirect |
| 11. C2×Dic842 | C22 | semidirect |
| 20. #20269755 | C22 | semidirect |
| 23. M16×C421 | C22 | semidirect |
| 24. C42×C421 | C22 | semidirect |
| 64. C421 | #455 | semidirect |
| 71. #104 | D421 | semidirect |
| 87. M16 | C2×D421 | semidirect |
| 89. C42 | C2×D421 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27212412 | 2 |
| #27212399 | 2 |
| #27212396 | 2 |
| #27212354 | 2 |
| #27212294 | 2 |
| #27212282 | 2 |
| #104×C421 | 2 |
| #455 | 421 |