Finite Group DatabasebetaFinite Group DatabasebetaOrder 2624.
238 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 97 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×D41 |
| commutator, socle, cosocle | C22×C41 | C24 |
| Fitting | C4×D4×C41 | C2 |
| hypercenter | C4×D4 | D41 |
| hypocenter | C41 | #553 |
| LCS | G ▷ C22×C41 ▷ C41 | |
| UCS | C1 ◁ C22 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13050158 | C2 | semidirect |
| 2. #13050157 | C2 | semidirect |
| 3. #13050154 | C2 | semidirect |
| 4. #13050149 | C2 | semidirect |
| 5. #13050147 | C2 | semidirect |
| 6. #13050138 | C2 | semidirect |
| 7. #13050137 | C2 | semidirect |
| 8. #13050136 | C2 | semidirect |
| 9. #13050136 | C2 | semidirect |
| 10. C4×C22⋊D41 | C2 | semidirect |
| 11. #13050124 | C2 | semidirect |
| 12. #13050124 | C2 | semidirect |
| 13. #13050121 | C2 | semidirect |
| 14. C2×#10620279 | C2 | semidirect |
| 15. C4×D4×C41 | C2 | semidirect |
| 110. C41 | #553 | semidirect |
| 123. C4×D4 | D41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13050158 | 2 |
| #13050157 | 2 |
| #13050154 | 2 |
| #13050149 | 2 |
| #13050147 | 2 |
| #13050138 | 2 |
| #13050137 | 2 |
| #13050136 | 2 |
| C4×C22⋊D41 | 2 |
| #13050124 | 2 |
| #13050121 | 2 |
| C2×#10620279 | 2 |
| C4×D4×C41 | 2 |
| #553 | 41 |