Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
840 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 840 conjugacy classes of subgroups — too many to draw. Only its 189 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×#380 | C2 |
| prime radical | C22×C22⋊D29 | C22 |
| hypercenter | #380 | D29 |
| hypocenter | C29 | #2409 |
| LCS | G ▷ C23×C29 ▷ C29 | |
| UCS | C1 ◁ C23 ◁ #380 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×Dic58 | C2 | semidirect |
| 2. C2×#11745259 | C2 | semidirect |
| 4. #14271084 | C2 | semidirect |
| 5. #14271076 | C2 | semidirect |
| 6. #14271068 | C2 | semidirect |
| 8. #14271038 | C2 | semidirect |
| 9. C29×#380 | C2 | semidirect |
| 40. C2×C22⋊D29 | Q8 | semidirect |
| 54. C2×Dic58 | D4 | semidirect |
| 73. C22×D29 | C2×Q8 | semidirect |
| 93. C2×Dic29 | C2×Q8 | semidirect |
| 102. C22×C29 | C22⋊Q8 | semidirect |
| 128. #380 | D29 | semidirect |
| 157. C29 | #2409 | semidirect |
| 233. C22 | #11745259 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic58 | 2 |
| C2×#11745259 | 2 |
| C2×C4×C22⋊D29 | 2 |
| #14271084 | 2 |
| #14271076 | 2 |
| #14271068 | 2 |
| #14271040 | 2 |
| #14271038 | 2 |
| C29×#380 | 2 |
| #2409 | 29 |