Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
496 conjugacy classes of subgroups; only the 188 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 188 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×#1181 |
| commutator, socle | C22×C29 | C23×C4 |
| Fitting | C29×C4⋊Q8 | C4 |
| prime radical, cosocle | C22×D29 | C24 |
| hypercenter | C4⋊Q8 | #1181 |
| hypocenter | C29 | #2369 |
| LCS | G ▷ C22×C29 ▷ C29 | |
| UCS | C1 ◁ C22 ◁ C4⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 12. C29×C4⋊Q8 | C4 | semidirect |
| 13. #11745306 | C4 | semidirect |
| 15. #11745250 | C4 | semidirect |
| 17. #11745231 | C4 | semidirect |
| 32. C4⋊#1181 | Q8 | semidirect |
| 91. C4⋊Q8 | #1181 | semidirect |
| 101. C29 | #2369 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| (C2×#1181)⋊Q8 | 2 |
| #14272114 | 2 |
| C4⋊C4×#1181 | 2 |
| C4×C4⋊#1181 | 2 |
| C4⋊Q8×D29 | 2 |
| #2369 | 29 |