Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
330 conjugacy classes of subgroups; only the 256 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 256 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C97 | C24 |
| commutator | C22 | C23×C4×C97 |
| Frattini, cosocle | C2×C4 | C24×C97 |
| socle | C22×C97 | C23×C4 |
| prime radical | C23×C97 | C22×C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C97 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #446×C97 | C2 | semidirect |
| 3. C8×Q8×C97 | C2 | semidirect |
| 54. #2986 | C97 | direct (N × H) |
| 55. C97 | #2986 | direct (N × H) |
| 57. #446 | C2×C97 | semidirect |
| 58. C8×Q8 | C2×C97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #533×C97 | 2 |
| #446×C97 | 2 |
| C8×Q8×C97 | 2 |
| #433×C97 | 2 |
| #431×C97 | 2 |
| #2986 | 97 |