Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
1564 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 1564 conjugacy classes of subgroups — too many to draw. Only its 197 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, socle, cosocle | C23×C97 | C24 |
| Fitting | #379×C97 | C2 |
| hypercenter | #379 | D97 |
| hypocenter | C97 | #2403 |
| LCS | G ▷ C23×C97 ▷ C97 | |
| UCS | C1 ◁ C23 ◁ #379 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×C22⋊D97 | C2 | semidirect |
| 2. C2×#15690780 | C2 | semidirect |
| 3. #20260644 | C2 | semidirect |
| 4. #20260612 | C2 | semidirect |
| 5. #379×C97 | C2 | semidirect |
| 6. C24×D97 | C22 | semidirect |
| 7. C22×D388 | C22 | semidirect |
| 11. C22×C22⋊D97 | C22 | semidirect |
| 12. C23×Dic97 | C22 | semidirect |
| 14. C2×#13095488 | C22 | semidirect |
| 15. #15690717 | C22 | semidirect |
| 17. C2×C22⋊C4×C97 | C22 | semidirect |
| 18. C2×C22⋊C4×C97 | C22 | semidirect |
| 32. C2×C22⋊D97 | D4 | semidirect |
| 39. C24×C97 | D4 | semidirect |
| 64. C22×D97 | C2×D4 | semidirect |
| 72. C2×Dic97 | C2×D4 | semidirect |
| 81. C22×C97 | #120 | semidirect |
| 100. C97 | #2403 | semidirect |
| 105. #379 | D97 | semidirect |
| 116. C2×C22⋊C4 | C2×D97 | semidirect |
| 117. C2×C22⋊C4 | C2×D97 | semidirect |
| 126. C24 | D388 | semidirect |
| 187. C22 | #15690780 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C22⋊D97 | 2 |
| C2×#15690780 | 2 |
| #20260644 | 2 |
| #20260612 | 2 |
| #379×C97 | 2 |
| #2403 | 97 |