Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
336 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 59 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | #11745299 |
| commutator, cosocle | C42×C29 | C23 |
| Frattini | C42 | C22×D29 |
| Fitting | C29×#459 | C2 |
| socle | C22×C29 | #120 |
| hypercenter | #459 | D29 |
| hypocenter | C29 | #1619 |
| LCS | G ▷ C42×C29 ▷ C22×C29 ▷ C29 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #459 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. D4×D116 | C2 | semidirect |
| 2. #14271539 | C2 | semidirect |
| 3. #14271355 | C2 | semidirect |
| 4. #14270906 | C2 | semidirect |
| 5. D4⋊#6597 | C2 | semidirect |
| 6. #14270890 | C2 | semidirect |
| 7. C29×#459 | C2 | semidirect |
| 11. C29×#127 | C22 | semidirect |
| 20. C29×C4⋊C8 | C22 | semidirect |
| 23. C4⋊#6597 | C22 | semidirect |
| 24. C4×#6597 | C22 | semidirect |
| 67. D4×C29 | D8 | semidirect |
| 83. D116 | D8 | semidirect |
| 114. #459 | D29 | semidirect |
| 131. #127 | C2×D29 | semidirect |
| 138. C4⋊C8 | C2×D29 | semidirect |
| 142. C29 | #1619 | semidirect |
| 194. D4 | #90782 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×D116 | 2 |
| #14271539 | 2 |
| #14271355 | 2 |
| #14270906 | 2 |
| D4⋊#6597 | 2 |
| #14270890 | 2 |
| C29×#459 | 2 |
| #1619 | 29 |