Finite Group DatabasebetaFinite Group DatabasebetaOrder 2368.
154 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 54 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 | C4⋊C4×C37 | C4 |
| prime radical, cosocle | C22×D37 | C23 |
| hypercenter | C4⋊C4 | #3866 |
| hypocenter | C37 | #387 |
| LCS | G ▷ C22×C37 ▷ C37 | |
| UCS | C1 ◁ C22 ◁ C4⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 17. C4⋊C4×C37 | C4 | semidirect |
| 18. C4⋊Dic37 | C4 | semidirect |
| 19. #10596936 | C4 | semidirect |
| 20. #10596936 | C4 | semidirect |
| 71. C37 | #387 | semidirect |
| 90. C4⋊C4 | #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 |
| C4⋊C4×D37 | 2 |
| #387 | 37 |