Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
126 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 71 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C8 | C22×D97 |
| commutator, socle, prime radical | C22×C97 | C22×C8 |
| Fitting | #346×C97 | C2 |
| cosocle | C2×C8×C97 | C23 |
| hypercenter | #346 | D97 |
| hypocenter | C97 | #2183 |
| LCS | G ▷ C22×C97 ▷ C97 | |
| UCS | C1 ◁ C2×C8 ◁ #346 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 33. C16×C97 | Q8 | semidirect |
| 60. C97 | #2183 | semidirect |
| 93. C16 | Dic194 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×Dic194 | 2 |
| C4⋊#13095486 | 2 |
| #20260553 | 2 |
| #20260510 | 2 |
| C16×Dic97 | 2 |
| #346×C97 | 2 |
| #2183 | 97 |