Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
752 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 177 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×#390 | C2 |
| prime radical | C2×#11745302 | C2 |
| hypercenter | #390 | D29 |
| hypocenter | C29 | #2858 |
| LCS | G ▷ C23×C29 ▷ C29 | |
| UCS | C1 ◁ C23 ◁ #390 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#11745250 | C2 | semidirect |
| 3. C2×#11745247 | C2 | semidirect |
| 4. #14271066 | C2 | semidirect |
| 5. #14271065 | C2 | semidirect |
| 6. #14271064 | C2 | semidirect |
| 7. #14271063 | C2 | semidirect |
| 8. C42×Dic29 | C2 | semidirect |
| 9. C29×#390 | C2 | semidirect |
| 62. C4×Dic29 | D4 | semidirect |
| 114. C4×C29 | #124 | semidirect |
| 117. Dic29 | #124 | semidirect |
| 126. #390 | D29 | semidirect |
| 155. C29 | #2858 | semidirect |
| 243. C4 | #11745247 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745250 | 2 |
| C2×#11745302 | 2 |
| C2×#11745247 | 2 |
| #14271066 | 2 |
| #14271065 | 2 |
| #14271064 | 2 |
| #14271063 | 2 |
| C42×Dic29 | 2 |
| C29×#390 | 2 |
| #2858 | 29 |