Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
430 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 430 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 |
|---|---|---|
| 2. C2×#17988407 | C2 | semidirect |
| 5. #22610089 | C2 | semidirect |
| 6. #22608041 | C2 | semidirect |
| 7. C73×#1387 | C2 | semidirect |
| 12. #17988703 | C4 | semidirect |
| 73. Dic292 | C4⋊C4 | semidirect |
| 77. D584 | C4⋊C4 | semidirect |
| 164. #1387 | D73 | semidirect |
| 165. C73 | #12821 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988703 | 2 |
| C2×#17988407 | 2 |
| #22611644 | 2 |
| #22611641 | 2 |
| #22610089 | 2 |
| #22608041 | 2 |
| C73×#1387 | 2 |
| #12821 | 73 |