Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
188 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 51 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×#17988422 | C2 | semidirect |
| 2. #22612226 | C2 | semidirect |
| 3. #22612052 | C2 | semidirect |
| 4. #22612048 | C2 | semidirect |
| 5. #22608134 | C2 | semidirect |
| 6. #22608122 | C2 | semidirect |
| 7. C73×#1419 | C2 | semidirect |
| 100. #1419 | D73 | semidirect |
| 101. C73 | #13700 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988422 | 2 |
| #22612226 | 2 |
| #22612052 | 2 |
| #22612048 | 2 |
| #22608134 | 2 |
| #22608122 | 2 |
| C73×#1419 | 2 |
| #13700 | 73 |