Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
1116 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 1116 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, prime radical | C23×D4×C29 | C2 |
| hypercenter | C23×D4 | D29 |
| hypocenter | C29 | #2405 |
| LCS | G ▷ C23×C29 ▷ C29 | |
| UCS | C1 ◁ C23 ◁ C23×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#11745297 | C2 | semidirect |
| 2. C22×C22⋊Dic29 | C2 | semidirect |
| 3. #14271077 | C2 | semidirect |
| 4. #14271043 | C2 | semidirect |
| 5. #14271036 | C2 | semidirect |
| 6. #14271019 | C2 | semidirect |
| 7. #14271019 | C2 | semidirect |
| 16. C23×Dic29 | C22 | semidirect |
| 17. C23×Dic29 | C22 | semidirect |
| 21. C2×C22⋊Dic29 | C22 | semidirect |
| 22. C2×C22⋊Dic29 | C22 | semidirect |
| 23. C2×C22⋊Dic29 | C22 | semidirect |
| 24. C2×C22⋊Dic29 | C22 | semidirect |
| 25. C2×C22⋊Dic29 | C22 | semidirect |
| 27. C2×#90779 | C22 | semidirect |
| 28. #11745179 | C22 | semidirect |
| 126. C22×C29 | #123 | semidirect |
| 171. C29 | #2405 | semidirect |
| 267. C22 | #11745297 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745297 | 2 |
| C22×C22⋊Dic29 | 2 |
| #14271077 | 2 |
| #14271043 | 2 |
| #14271036 | 2 |
| #14271019 | 2 |
| C23×D4×C29 | 2 |
| #2405 | 29 |