Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
240 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 69 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. #22612154 | C2 | semidirect |
| 2. D4×#11924003 | C2 | semidirect |
| 3. #22609320 | C2 | semidirect |
| 4. #22608002 | C2 | semidirect |
| 5. #22607987 | C2 | semidirect |
| 6. #22607977 | C2 | semidirect |
| 121. C73 | #12467 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22612154 | 2 |
| D4×#11924003 | 2 |
| #22609320 | 2 |
| #22608002 | 2 |
| #22607987 | 2 |
| #22607977 | 2 |
| C73×#1667 | 2 |
| #12467 | 73 |