Finite Group DatabasebetaFinite Group DatabasebetaOrder 26944.
290 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D421 |
| commutator, socle, cosocle | C22×C421 | C24 |
| Fitting | #124×C421 | C2 |
| hypercenter | #124 | D421 |
| hypocenter | C421 | #548 |
| LCS | G ▷ C22×C421 ▷ C421 | |
| UCS | C1 ◁ C22 ◁ #124 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#20269770 | C2 | semidirect |
| 2. C2×Q8×D421 | C2 | semidirect |
| 3. #27212352 | C2 | semidirect |
| 4. #27212343 | C2 | semidirect |
| 5. #27212342 | C2 | semidirect |
| 6. #27212339 | C2 | semidirect |
| 7. #27212337 | C2 | semidirect |
| 8. C4×Dic842 | C2 | semidirect |
| 9. C4×D1684 | C2 | semidirect |
| 10. #27212326 | C2 | semidirect |
| 11. #124×C421 | C2 | semidirect |
| 40. Dic842 | D4 | semidirect |
| 68. C2×D421 | #41 | semidirect |
| 83. C421 | #548 | semidirect |
| 88. #124 | D421 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20269770 | 2 |
| C2×Q8×D421 | 2 |
| #27212352 | 2 |
| #27212343 | 2 |
| #27212342 | 2 |
| #27212339 | 2 |
| #27212337 | 2 |
| C4×Dic842 | 2 |
| C4×D1684 | 2 |
| #27212326 | 2 |
| #124×C421 | 2 |
| #548 | 421 |