Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
360 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 198 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C23×#1181 |
| commutator, socle | C2×C29 | C23×C8 |
| Fitting | C29×#131 | C4 |
| prime radical | #41×D29 | C4 |
| cosocle | #6597 | C24 |
| hypercenter | #131 | #1181 |
| hypocenter | C29 | #3407 |
| LCS | G ▷ C2×C29 ▷ C29 | |
| UCS | C1 ◁ C4 ◁ #131 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14272222 | C2 | semidirect |
| 2. #14272221 | C2 | semidirect |
| 3. C2×#11745206 | C2 | semidirect |
| 4. D29⋊M32 | C2 | semidirect |
| 13. #11745214 | C22 | semidirect |
| 14. C2×#90770 | C22 | semidirect |
| 17. #11745206 | C22 | semidirect |
| 18. D29⋊C16 | C22 | semidirect |
| 84. C29 | #3407 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272222 | 2 |
| #14272221 | 2 |
| C2×#11745206 | 2 |
| D29⋊M32 | 2 |
| #131×D29 | 2 |
| #3407 | 29 |