Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
218 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 63 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. #22612204 | C2 | semidirect |
| 5. #22608004 | C2 | semidirect |
| 6. #22607985 | C2 | semidirect |
| 7. C73×#1364 | C2 | semidirect |
| 58. #11924003 | SD16 | semidirect |
| 111. #1364 | D73 | semidirect |
| 112. C73 | #12454 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22612204 | 2 |
| #22611762 | 2 |
| #22609321 | 2 |
| #22609317 | 2 |
| #22608004 | 2 |
| #22607985 | 2 |
| C73×#1364 | 2 |
| #12454 | 73 |