Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1854 conjugacy classes of subgroups; only the 272 normal subgroups are shown.
This group has 1854 conjugacy classes of subgroups — too many to draw. Only its 272 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×#17989531 | C2 | semidirect |
| 2. #22625121 | C2 | semidirect |
| 3. #22625114 | C2 | semidirect |
| 14. C2×#14556580 | C4 | semidirect |
| 15. C2×#14556579 | C4 | semidirect |
| 16. C2×#14556578 | C4 | semidirect |
| 17. C2×#14556577 | C4 | semidirect |
| 21. C2×#124×C73 | C4 | semidirect |
| 96. C4×Dic73 | C22⋊C4 | semidirect |
| 97. C4×Dic73 | C22⋊C4 | semidirect |
| 107. C42×C73 | C22⋊C4 | semidirect |
| 192. C73 | #14662 | semidirect |
| 200. C2×#124 | #64408 | semidirect |
| 294. C42 | C22⋊#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989531 | 2 |
| #22625121 | 2 |
| #22625114 | 2 |
| #22625113 | 2 |
| C2×#124×D73 | 2 |
| #14662 | 73 |