Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
1088 conjugacy classes of subgroups; only the 261 normal subgroups are shown.
This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 261 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 | #379×C97 | C2 |
| socle, cosocle | C23×C97 | C24 |
| prime radical | C25×C97 | C22 |
| hypercenter | #379 | D97 |
| hypocenter | C97 | #2280 |
| LCS | G ▷ C22×C97 ▷ C97 | |
| UCS | C1 ◁ C23 ◁ #379 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#15690766 | C2 | semidirect |
| 3. #20260596 | C2 | semidirect |
| 4. #20260593 | C2 | semidirect |
| 6. C22⋊C4×Dic97 | C2 | semidirect |
| 9. C23×Dic97 | C4 | semidirect |
| 15. C2×#13095490 | C22 | semidirect |
| 18. C2×C4×Dic97 | C22 | semidirect |
| 19. #15690717 | C22 | semidirect |
| 67. C2×Dic97 | C22⋊C4 | semidirect |
| 80. C22×C97 | #117 | semidirect |
| 95. C97 | #2280 | semidirect |
| 175. C22 | #15690766 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×Dic97 | 2 |
| C2×#15690766 | 2 |
| #20260596 | 2 |
| #20260593 | 2 |
| #20260591 | 2 |
| C22⋊C4×Dic97 | 2 |
| #379×C97 | 2 |
| #2280 | 97 |