Finite Group DatabasebetaFinite Group DatabasebetaOrder 25408.
216 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 216 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 | C4×Q8×C397 | C2 |
| prime radical | #27163071 | C2 |
| hypercenter | C4×Q8 | D397 |
| hypocenter | C397 | #542 |
| LCS | G ▷ C22×C397 ▷ C397 | |
| UCS | C1 ◁ C22 ◁ C4×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #27163095 | C2 | semidirect |
| 2. #27163090 | C2 | semidirect |
| 3. #27163085 | C2 | semidirect |
| 4. #27163084 | C2 | semidirect |
| 5. #27163081 | C2 | semidirect |
| 6. #27163074 | C2 | semidirect |
| 7. #27163072 | C2 | semidirect |
| 9. C4×D1588 | C2 | semidirect |
| 10. #27163053 | C2 | semidirect |
| 11. C4×Q8×C397 | C2 | semidirect |
| 73. C397 | #542 | semidirect |
| 83. C4×Q8 | D397 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27163095 | 2 |
| #27163090 | 2 |
| #27163085 | 2 |
| #27163084 | 2 |
| #27163081 | 2 |
| #27163074 | 2 |
| #27163072 | 2 |
| #27163071 | 2 |
| C4×D1588 | 2 |
| #27163053 | 2 |
| C4×Q8×C397 | 2 |
| #542 | 397 |