Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
280 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D97 |
| commutator, socle, prime radical | C23×C97 | C22×C4 |
| Fitting | #336×C97 | C2 |
| cosocle | C22×C4×C97 | C23 |
| hypercenter | #336 | D97 |
| hypocenter | C97 | #1985 |
| LCS | G ▷ C23×C97 ▷ C97 | |
| UCS | C1 ◁ C22×C4 ◁ #336 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 35. C2×#11715895 | Q8 | semidirect |
| 51. C2×C8×C97 | Q8 | semidirect |
| 109. C97 | #1985 | semidirect |
| 153. C2×C8 | Dic194 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic194 | 2 |
| C2×#15690739 | 2 |
| C2×#15690720 | 2 |
| #20260490 | 2 |
| #20260489 | 2 |
| #336×C97 | 2 |
| #1985 | 97 |