Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
504 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 189 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D97 |
| commutator, socle, prime radical, cosocle | C23×C97 | C24 |
| Frattini | C23 | C23×D97 |
| Fitting | #376×C97 | C2 |
| hypercenter | #376 | D97 |
| hypocenter | C97 | #2399 |
| LCS | G ▷ C23×C97 ▷ C97 | |
| UCS | C1 ◁ C22×C4 ◁ #376 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 29. C42×C97 | Q8 | semidirect |
| 55. C97 | #2399 | semidirect |
| 83. C42 | 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 |
| #20260667 | 2 |
| #20260656 | 2 |
| C4×C4⋊Dic97 | 2 |
| #376×C97 | 2 |
| #2399 | 97 |