Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
3464 conjugacy classes of subgroups; only the 365 normal subgroups are shown.
This group has 3464 conjugacy classes of subgroups — too many to draw. Only its 365 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×D97 | C2 |
| hypercenter | #379 | D97 |
| hypocenter | C97 | C2×#379 |
| 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×C22⋊C4×D97 | C2 | semidirect |
| 3. #20260591 | C2 | semidirect |
| 4. #20260590 | C2 | semidirect |
| 5. #379×C97 | C2 | semidirect |
| 7. C24×D97 | C4 | semidirect |
| 10. C22×C4×D97 | C22 | semidirect |
| 11. C2×C22⋊Dic97 | C22 | semidirect |
| 12. C2×#13095488 | C22 | semidirect |
| 15. C2×C22⋊C4×C97 | C22 | semidirect |
| 22. C23×D97 | C2×C4 | semidirect |
| 26. C22×Dic97 | C23 | semidirect |
| 31. C24×C97 | C2×C4 | semidirect |
| 33. C22×C4×C97 | C23 | semidirect |
| 48. C22×D97 | C22⋊C4 | semidirect |
| 59. C22×C97 | C2×C22⋊C4 | semidirect |
| 67. C2×D97 | C2×C22⋊C4 | semidirect |
| 75. D97 | #379 | direct (N × H) |
| 77. C97 | C2×#379 | semidirect |
| 82. #379 | D97 | direct (N × H) |
| 92. C2×C22⋊C4 | C2×D97 | semidirect |
| 104. C24 | C4×D97 | semidirect |
| 108. C22×C4 | C22×D97 | semidirect |
| 143. C22 | C22⋊C4×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×D97 | 2 |
| C2×C22⋊C4×D97 | 2 |
| #20260591 | 2 |
| #20260590 | 2 |
| #379×C97 | 2 |
| C2×#379 | 97 |