Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
422 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 107 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. #22611720 | C2 | semidirect |
| 5. #22610675 | C2 | semidirect |
| 6. #22608014 | C2 | semidirect |
| 7. C73×#1386 | C2 | semidirect |
| 21. #17988396 | C4 | semidirect |
| 49. #14556531 | C2×C4 | semidirect |
| 70. #106×C73 | C2×C4 | semidirect |
| 85. Dic292 | C4⋊C4 | semidirect |
| 89. D584 | C4⋊C4 | semidirect |
| 187. #1386 | D73 | semidirect |
| 189. C73 | #12943 | semidirect |
| 245. #106 | C4×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22618731 | 2 |
| #22611720 | 2 |
| C2×#17988396 | 2 |
| #22611644 | 2 |
| #22610675 | 2 |
| #22608014 | 2 |
| C73×#1386 | 2 |
| #12943 | 73 |