Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
520 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 130 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 | C22×#87604 |
| commutator, socle | C23×C97 | C22×C4 |
| Fitting | #95×C97 | C4 |
| prime radical, cosocle | C23×D97 | C23 |
| hypercenter | #95 | #87604 |
| hypocenter | C97 | #1442 |
| LCS | G ▷ C23×C97 ▷ C97 | |
| UCS | C1 ◁ C23 ◁ #95 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 16. #15690717 | C4 | semidirect |
| 17. #15690717 | C4 | semidirect |
| 18. #95×C97 | C4 | semidirect |
| 139. C97 | #1442 | semidirect |
| 157. #95 | #87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊#87604 | 2 |
| C2×(C2×#87604)⋊C4 | 2 |
| #95×D97 | 2 |
| #1442 | 97 |