Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
476 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 2. #22618815 | C2 | semidirect |
| 3. C2×#17988398 | C2 | semidirect |
| 4. #22610827 | C2 | semidirect |
| 5. #22608036 | C2 | semidirect |
| 6. #22608016 | C2 | semidirect |
| 7. C73×#2145 | C2 | semidirect |
| 11. #17989027 | C4 | semidirect |
| 13. #17989022 | C4 | semidirect |
| 34. C2×Dic292 | C2×C4 | semidirect |
| 36. C2×D584 | C2×C4 | semidirect |
| 50. #14556531 | C2×C4 | semidirect |
| 192. #2145 | D73 | semidirect |
| 197. C73 | #13030 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22623065 | 2 |
| #22618815 | 2 |
| C2×#17988398 | 2 |
| #22610827 | 2 |
| #22608036 | 2 |
| #22608016 | 2 |
| C73×#2145 | 2 |
| #13030 | 73 |