Finite Group DatabasebetaFinite Group DatabasebetaOrder 2368.
322 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 143 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×Dic74 | C2 | semidirect |
| 2. #11924515 | C2 | direct (N × H) |
| 3. C2×C4⋊Dic37 | C2 | semidirect |
| 4. C2×#10596936 | C2 | semidirect |
| 15. C2×Dic74 | C22 | semidirect |
| 17. C4⋊Dic37 | C22 | semidirect |
| 18. #10596936 | C22 | semidirect |
| 21. C23×C37 | Q8 | semidirect |
| 39. C22×C37 | C2×Q8 | semidirect |
| 47. C2×C37 | C22⋊Q8 | semidirect |
| 52. C37 | C2×C22⋊Q8 | semidirect |
| 73. C23 | Dic74 | semidirect |
| 90. C22 | C2×Dic74 | semidirect |
| 99. C2 | #11924515 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic74 | 2 |
| #11924515 | 2 |
| C2×C4⋊Dic37 | 2 |
| C2×#10596936 | 2 |
| C2×C22⋊Dic37 | 2 |
| C23×C4×C37 | 2 |
| C2×C22⋊Q8 | 37 |