Finite Group DatabasebetaFinite Group DatabasebetaOrder 2368.
186 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 64 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 | C22×#3866 |
| commutator, socle | C22×C37 | C22×C4 |
| Fitting | C2×Q8×C37 | C4 |
| prime radical, cosocle | C22×D37 | C23 |
| hypercenter | C2×Q8 | #3866 |
| hypocenter | C37 | #391 |
| LCS | G ▷ C22×C37 ▷ C37 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 7. C2×Q8×C37 | C4 | semidirect |
| 12. C2×Dic74 | C4 | semidirect |
| 13. C2×Dic74 | C4 | semidirect |
| 21. C2×#3866 | Q8 | semidirect |
| 50. C37 | #391 | semidirect |
| 59. C2×Q8 | #3866 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊#3866 | 2 |
| C2×C4×#3866 | 2 |
| (C2×#3866)⋊C4 | 2 |
| C2×Q8×D37 | 2 |
| #391 | 37 |