Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
408 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 165 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 | C43×C97 | C2 |
| hypercenter | C43 | D97 |
| hypocenter | C97 | #2863 |
| LCS | G ▷ C23×C97 ▷ C97 | |
| UCS | C1 ◁ C23 ◁ C43 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 25. C42×C97 | Q8 | semidirect |
| 50. C97 | #2863 | semidirect |
| 75. C42 | Dic194 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20260641 | 2 |
| #20260633 | 2 |
| #20260619 | 2 |
| #20260603 | 2 |
| C43×C97 | 2 |
| #2863 | 97 |