Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
780 conjugacy classes of subgroups; only the 325 normal subgroups are shown.
This group has 780 conjugacy classes of subgroups — too many to draw. Only its 325 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 | C2×C29 | C22×C42 |
| Fitting | C29×#376 | C2 |
| socle, cosocle | C23×C29 | C24 |
| prime radical | C22×D116 | C22 |
| hypercenter | #376 | D29 |
| hypocenter | C29 | #2275 |
| LCS | G ▷ C2×C29 ▷ C29 | |
| UCS | C1 ◁ C23 ◁ #376 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×C4⋊Dic29 | C2 | semidirect |
| 3. #14271010 | C2 | semidirect |
| 4. #95×D29 | C2 | semidirect |
| 5. C29×#376 | C2 | semidirect |
| 12. C4×D116 | C4 | semidirect |
| 23. C2×C4×D29 | C2×C4 | semidirect |
| 24. C42×C29 | C2×C4 | semidirect |
| 25. #90781 | C2×C4 | semidirect |
| 26. C4⋊Dic29 | C2×C4 | semidirect |
| 40. D116 | C42 | semidirect |
| 56. #376 | D29 | semidirect |
| 72. C29 | #2275 | semidirect |
| 84. C42 | C4×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D116 | 2 |
| C4×C4⋊Dic29 | 2 |
| #14271010 | 2 |
| #95×D29 | 2 |
| C29×#376 | 2 |
| #2275 | 29 |