Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
170 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 55 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. #22612208 | C2 | semidirect |
| 3. #22608132 | C2 | semidirect |
| 4. #22608126 | C2 | semidirect |
| 7. C73×#1423 | C2 | semidirect |
| 82. #1423 | D73 | semidirect |
| 86. C73 | #13707 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22612208 | 2 |
| #22611777 | 2 |
| #22608132 | 2 |
| #22608126 | 2 |
| #22608110 | 2 |
| #22608108 | 2 |
| C73×#1423 | 2 |
| #13707 | 73 |