Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
588 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 249 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 | C22×C97 | C23×C4 |
| Fitting | #384×C97 | C2 |
| socle, prime radical, cosocle | C23×C97 | C24 |
| hypercenter | #384 | D97 |
| hypocenter | C97 | C4×C4⋊Q8 |
| LCS | G ▷ C22×C97 ▷ C97 | |
| UCS | C1 ◁ C23 ◁ #384 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 9. #15690810 | C4 | semidirect |
| 35. C4×Dic97 | Q8 | semidirect |
| 69. C4×C97 | C4×Q8 | semidirect |
| 73. Dic97 | C4⋊Q8 | semidirect |
| 80. C97 | C4×C4⋊Q8 | semidirect |
| 153. C4 | #15690775 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690810 | 2 |
| C2×#15690775 | 2 |
| #20260640 | 2 |
| #20260631 | 2 |
| C4⋊C4×Dic97 | 2 |
| C42×Dic97 | 2 |
| #384×C97 | 2 |
| C4×C4⋊Q8 | 97 |