Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
224 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 71 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. #22612204 | C2 | semidirect |
| 4. #22608002 | C2 | semidirect |
| 5. #22607987 | C2 | semidirect |
| 6. #22607986 | C2 | semidirect |
| 51. #11924003 | SD16 | semidirect |
| 112. C73 | #12451 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22612204 | 2 |
| D4×#11924003 | 2 |
| #22609320 | 2 |
| #22608002 | 2 |
| #22607987 | 2 |
| #22607986 | 2 |
| C73×#1673 | 2 |
| #12451 | 73 |