Finite Group DatabasebetaFinite Group DatabasebetaOrder 2624.
248 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 95 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 | #124×C41 | C2 |
| prime radical | #13050132 | C2 |
| hypercenter | #124 | D41 |
| hypocenter | C41 | #551 |
| LCS | G ▷ C22×C41 ▷ C41 | |
| UCS | C1 ◁ C22 ◁ #124 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13050157 | C2 | semidirect |
| 2. #13050146 | C2 | semidirect |
| 3. #13050145 | C2 | semidirect |
| 4. #13050140 | C2 | semidirect |
| 6. #13050124 | C2 | semidirect |
| 7. #13050121 | C2 | semidirect |
| 8. C22⋊C4×D41 | C2 | semidirect |
| 9. #124×C41 | C2 | semidirect |
| 11. C2×Q8×C41 | C22 | semidirect |
| 14. C22×Dic41 | C22 | semidirect |
| 18. C22⋊C4×C41 | C22 | semidirect |
| 19. C42×C41 | C22 | semidirect |
| 22. C22⋊Dic41 | C22 | semidirect |
| 26. C4⋊Dic41 | C22 | semidirect |
| 27. #10620279 | C22 | semidirect |
| 28. #10620279 | C22 | semidirect |
| 29. #10620279 | C22 | semidirect |
| 30. C4×Dic41 | C22 | semidirect |
| 69. C41 | #551 | semidirect |
| 71. #124 | D41 | semidirect |
| 80. C2×Q8 | C2×D41 | semidirect |
| 97. C22⋊C4 | C2×D41 | semidirect |
| 99. C42 | C2×D41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13050157 | 2 |
| #13050146 | 2 |
| #13050145 | 2 |
| #13050140 | 2 |
| #13050132 | 2 |
| #13050124 | 2 |
| #13050121 | 2 |
| C22⋊C4×D41 | 2 |
| #124×C41 | 2 |
| #551 | 41 |