Finite Group DatabasebetaFinite Group DatabasebetaOrder 25408.
250 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 250 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 | C22⋊Q8×C397 | C2 |
| hypercenter | C22⋊Q8 | D397 |
| hypocenter | C397 | #538 |
| LCS | G ▷ C22×C397 ▷ C397 | |
| UCS | C1 ◁ C22 ◁ C22⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #27163091 | C2 | semidirect |
| 2. #27163085 | C2 | semidirect |
| 3. #27163081 | C2 | semidirect |
| 4. #27163071 | C2 | semidirect |
| 5. #27163070 | C2 | semidirect |
| 6. #27163066 | C2 | semidirect |
| 7. #27163056 | C2 | semidirect |
| 8. C2×#20263708 | C2 | semidirect |
| 9. C22⋊Q8×C397 | C2 | semidirect |
| 13. C2×D1588 | C22 | semidirect |
| 16. C2×C4×D397 | C22 | semidirect |
| 17. C4⋊Dic397 | C22 | semidirect |
| 18. #20263710 | C22 | semidirect |
| 23. #20263708 | C22 | semidirect |
| 24. #20263708 | C22 | semidirect |
| 25. C4×Dic397 | C22 | semidirect |
| 26. C2×Q8×C397 | C22 | semidirect |
| 28. C4⋊C4×C397 | C22 | semidirect |
| 29. C4⋊C4×C397 | C22 | semidirect |
| 74. C397 | #538 | semidirect |
| 79. C22⋊Q8 | D397 | semidirect |
| 86. C2×Q8 | C2×D397 | semidirect |
| 96. C4⋊C4 | C2×D397 | semidirect |
| 97. C4⋊C4 | C2×D397 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27163091 | 2 |
| #27163085 | 2 |
| #27163081 | 2 |
| #27163071 | 2 |
| #27163070 | 2 |
| #27163066 | 2 |
| #27163056 | 2 |
| C2×#20263708 | 2 |
| C22⋊Q8×C397 | 2 |
| #538 | 397 |