Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
400 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 157 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, socle, prime radical, cosocle | C23×C97 | C24 |
| Fitting | #382×C97 | C2 |
| hypercenter | #382 | D97 |
| hypocenter | C97 | #2864 |
| LCS | G ▷ C23×C97 ▷ C97 | |
| UCS | C1 ◁ C23 ◁ #382 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 77. C97 | #2864 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20260634 | 2 |
| #20260631 | 2 |
| #20260622 | 2 |
| #20260618 | 2 |
| #20260601 | 2 |
| C42×Dic97 | 2 |
| #382×C97 | 2 |
| #2864 | 97 |