Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
472 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 197 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 | #384×C97 | C2 |
| hypercenter | #384 | D97 |
| hypocenter | C97 | #2859 |
| LCS | G ▷ C23×C97 ▷ C97 | |
| UCS | C1 ◁ C23 ◁ #384 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 63. C4×C97 | #125 | semidirect |
| 75. C97 | #2859 | semidirect |
| 142. C4 | #15690801 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690801 | 2 |
| #20260634 | 2 |
| #20260631 | 2 |
| #20260605 | 2 |
| #20260600 | 2 |
| C42×Dic97 | 2 |
| #384×C97 | 2 |
| #2859 | 97 |