Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
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×D29 |
| commutator, socle, cosocle | C23×C29 | C24 |
| Fitting | C29×#379 | C2 |
| hypercenter | #379 | D29 |
| hypocenter | C29 | #2403 |
| LCS | G ▷ C23×C29 ▷ C29 | |
| UCS | C1 ◁ C23 ◁ #379 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×C22⋊D29 | C2 | semidirect |
| 2. C2×#11745244 | C2 | semidirect |
| 3. #14271072 | C2 | semidirect |
| 4. #14271040 | C2 | semidirect |
| 5. C29×#379 | C2 | semidirect |
| 7. C24×D29 | C22 | semidirect |
| 11. C22×C22⋊D29 | C22 | semidirect |
| 12. C23×Dic29 | C22 | semidirect |
| 13. C22×D116 | C22 | semidirect |
| 14. C2×C22⋊C4×C29 | C22 | semidirect |
| 15. C2×C22⋊C4×C29 | C22 | semidirect |
| 16. C2×#90781 | C22 | semidirect |
| 18. #11745179 | C22 | semidirect |
| 21. C24×C29 | D4 | semidirect |
| 36. C2×C22⋊D29 | D4 | semidirect |
| 64. C22×D29 | C2×D4 | semidirect |
| 72. C2×Dic29 | C2×D4 | semidirect |
| 82. C22×C29 | #120 | semidirect |
| 98. #379 | D29 | semidirect |
| 115. C2×C22⋊C4 | C2×D29 | semidirect |
| 116. C2×C22⋊C4 | C2×D29 | semidirect |
| 118. C29 | #2403 | semidirect |
| 126. C24 | D116 | semidirect |
| 187. C22 | #11745244 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C22⋊D29 | 2 |
| C2×#11745244 | 2 |
| #14271072 | 2 |
| #14271040 | 2 |
| C29×#379 | 2 |
| #2403 | 29 |