Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
1240 conjugacy classes of subgroups; only the 501 normal subgroups are shown.
This group has 1240 conjugacy classes of subgroups — too many to draw. Only its 501 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D29 |
| commutator, cosocle | C22×C29 | C25 |
| Frattini | C22 | C24×D29 |
| Fitting | C2×C29×C4⋊Q8 | C2 |
| socle | C23×C29 | C24 |
| hypercenter | C2×C4⋊Q8 | D29 |
| hypocenter | C29 | C2×#555 |
| LCS | G ▷ C22×C29 ▷ C29 | |
| UCS | C1 ◁ C23 ◁ C2×C4⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14271879 | C2 | direct (N × H) |
| 2. C2×#11745309 | C2 | semidirect |
| 3. C2×#11745257 | C2 | semidirect |
| 4. C2×C4×D116 | C2 | semidirect |
| 5. C2×#11745254 | C2 | semidirect |
| 6. C2×C29×C4⋊Q8 | C2 | semidirect |
| 11. C29×C4⋊Q8 | C22 | semidirect |
| 14. #11745309 | C22 | semidirect |
| 19. #11745257 | C22 | semidirect |
| 20. #11745254 | C22 | semidirect |
| 21. C4×D116 | C22 | semidirect |
| 71. C2×C4⋊Q8 | D29 | semidirect |
| 76. C2×C29 | #555 | semidirect |
| 84. C4⋊Q8 | C2×D29 | semidirect |
| 95. C29 | C2×#555 | semidirect |
| 144. C2 | #14271879 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271879 | 2 |
| C2×#11745309 | 2 |
| C2×#11745257 | 2 |
| C2×C4×D116 | 2 |
| C2×#11745254 | 2 |
| C2×C29×C4⋊Q8 | 2 |
| C2×#555 | 29 |