Finite Group DatabasebetaFinite Group DatabasebetaOrder 25408.
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×D397 |
| commutator, socle, cosocle | C22×C397 | C24 |
| Fitting | #124×C397 | C2 |
| prime radical | #27163064 | C2 |
| hypercenter | #124 | D397 |
| hypocenter | C397 | #551 |
| LCS | G ▷ C22×C397 ▷ C397 | |
| UCS | C1 ◁ C22 ◁ #124 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #27163089 | C2 | semidirect |
| 2. #27163078 | C2 | semidirect |
| 3. #27163077 | C2 | semidirect |
| 4. #27163072 | C2 | semidirect |
| 6. #27163056 | C2 | semidirect |
| 7. #27163053 | C2 | semidirect |
| 8. C22⋊C4×D397 | C2 | semidirect |
| 9. #124×C397 | C2 | semidirect |
| 12. C22×Dic397 | C22 | semidirect |
| 15. C4⋊Dic397 | C22 | semidirect |
| 16. #20263710 | C22 | semidirect |
| 17. #20263710 | C22 | semidirect |
| 18. #20263710 | C22 | semidirect |
| 21. C22⋊Dic397 | C22 | semidirect |
| 25. C4×Dic397 | C22 | semidirect |
| 26. C2×Q8×C397 | C22 | semidirect |
| 29. C22⋊C4×C397 | C22 | semidirect |
| 30. C42×C397 | C22 | semidirect |
| 68. C397 | #551 | semidirect |
| 71. #124 | D397 | semidirect |
| 80. C2×Q8 | C2×D397 | semidirect |
| 97. C22⋊C4 | C2×D397 | semidirect |
| 99. C42 | C2×D397 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27163089 | 2 |
| #27163078 | 2 |
| #27163077 | 2 |
| #27163072 | 2 |
| #27163064 | 2 |
| #27163056 | 2 |
| #27163053 | 2 |
| C22⋊C4×D397 | 2 |
| #124×C397 | 2 |
| #551 | 397 |