Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
736 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 736 conjugacy classes of subgroups — too many to draw. Only its 209 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C22×D97 |
| commutator | C23×C97 | C22×C4 |
| Fitting | C2×#95×C97 | C2 |
| socle, prime radical, cosocle | C24×C97 | C23 |
| hypercenter | C2×#95 | D97 |
| hypocenter | C97 | #1446 |
| LCS | G ▷ C23×C97 ▷ C97 | |
| UCS | C1 ◁ C24 ◁ C2×#95 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 8. C22×Dic194 | C4 | semidirect |
| 29. C22×Dic97 | Q8 | semidirect |
| 39. C22×C4×C97 | Q8 | semidirect |
| 97. C97 | #1446 | semidirect |
| 133. C22×C4 | Dic194 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic194 | 2 |
| C2×#15690717 | 2 |
| C2×#95×C97 | 2 |
| #1446 | 97 |