Finite Group DatabasebetaFinite Group DatabasebetaOrder 2368.
228 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 107 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. #11924535 | C2 | semidirect |
| 2. #11924526 | C2 | semidirect |
| 3. #11924516 | C2 | semidirect |
| 4. #11924515 | C2 | semidirect |
| 5. #11924515 | C2 | semidirect |
| 6. #11924514 | C2 | semidirect |
| 7. #11924501 | C2 | semidirect |
| 10. C4⋊C4×D37 | C2 | semidirect |
| 11. C2×C4⋊C4×C37 | C2 | semidirect |
| 43. C22⋊D37 | Q8 | semidirect |
| 75. C37 | #554 | semidirect |
| 86. C2×C4⋊C4 | D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11924535 | 2 |
| #11924526 | 2 |
| #11924516 | 2 |
| #11924515 | 2 |
| #11924514 | 2 |
| #11924501 | 2 |
| C4×C22⋊D37 | 2 |
| C4⋊C4×D37 | 2 |
| C2×C4⋊C4×C37 | 2 |
| #554 | 37 |