Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
492 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 109 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. #22618539 | C2 | semidirect |
| 3. C2×#17988401 | C2 | semidirect |
| 4. C2×#17988399 | C2 | semidirect |
| 5. #22611560 | C2 | semidirect |
| 6. #22608042 | C2 | semidirect |
| 7. C73×#1385 | C2 | semidirect |
| 175. #1385 | D73 | semidirect |
| 176. C73 | #13007 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988858 | 2 |
| #22618539 | 2 |
| C2×#17988401 | 2 |
| C2×#17988399 | 2 |
| #22611560 | 2 |
| #22608042 | 2 |
| C73×#1385 | 2 |
| #13007 | 73 |