Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
1492 conjugacy classes of subgroups; only the 553 normal subgroups are shown.
This group has 1492 conjugacy classes of subgroups — too many to draw. Only its 553 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D29 |
| commutator, socle, cosocle | C22×C29 | C25 |
| Fitting | C29×#519 | C2 |
| hypercenter | #519 | D29 |
| hypocenter | C29 | #3486 |
| LCS | G ▷ C22×C29 ▷ C29 | |
| UCS | C1 ◁ C22 ◁ #519 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#11745362 | C2 | semidirect |
| 2. C22×Q8×D29 | C2 | semidirect |
| 3. Q8×D116 | C2 | semidirect |
| 4. #14271825 | C2 | semidirect |
| 5. #14271739 | C2 | semidirect |
| 6. #14271675 | C2 | semidirect |
| 7. C29×#519 | C2 | semidirect |
| 10. C2×#90809 | C22 | semidirect |
| 13. C2×Q8×D29 | C22 | semidirect |
| 17. C4×Q8×C29 | C22 | semidirect |
| 20. #11745259 | C22 | semidirect |
| 24. #11745237 | C22 | semidirect |
| 26. #11745231 | C22 | semidirect |
| 28. C2×Q8×C29 | D4 | semidirect |
| 79. C2×D29 | 2−1+4 | semidirect |
| 90. #519 | D29 | semidirect |
| 112. C4×Q8 | C2×D29 | semidirect |
| 115. C29 | #3486 | semidirect |
| 124. C2×Q8 | D116 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745362 | 2 |
| C22×Q8×D29 | 2 |
| Q8×D116 | 2 |
| #14271825 | 2 |
| #14271739 | 2 |
| #14271675 | 2 |
| C29×#519 | 2 |
| #3486 | 29 |