Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
466 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 115 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. C2×#17988400 | C2 | semidirect |
| 2. #22611667 | C2 | semidirect |
| 3. #22611659 | C2 | semidirect |
| 4. #22611647 | C2 | semidirect |
| 5. #22611536 | C2 | semidirect |
| 6. #22610055 | C2 | semidirect |
| 24. #495×C73 | C4 | semidirect |
| 25. #493×C73 | C4 | semidirect |
| 32. #14556531 | D4 | semidirect |
| 34. C2×#11924003 | D4 | semidirect |
| 182. C73 | #13215 | semidirect |
| 190. #495 | Dic73 | semidirect |
| 191. #493 | Dic73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988400 | 2 |
| #22611667 | 2 |
| #22611659 | 2 |
| #22611647 | 2 |
| #22611536 | 2 |
| #22610055 | 2 |
| C73×#3155 | 2 |
| #13215 | 73 |