Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
448 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 221 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D97 |
| commutator | C22×C97 | C23×C4 |
| Fitting | C2×#125×C97 | C2 |
| socle, prime radical, cosocle | C23×C97 | C24 |
| hypercenter | C2×#125 | D97 |
| hypocenter | C97 | #2371 |
| LCS | G ▷ C22×C97 ▷ C97 | |
| UCS | C1 ◁ C23 ◁ C2×#125 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 14. #125×C97 | C4 | semidirect |
| 55. C97 | #2371 | semidirect |
| 61. #125 | Dic97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20260621 | 2 |
| C4⋊C4×Dic97 | 2 |
| #20260581 | 2 |
| C2×#125×C97 | 2 |
| #2371 | 97 |