Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
408 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 91 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. C2×#17988414 | C2 | semidirect |
| 3. C2×#17988393 | C2 | semidirect |
| 4. #22611644 | C2 | semidirect |
| 5. C2×#17988372 | C2 | semidirect |
| 6. #22609992 | C2 | semidirect |
| 7. C73×#1387 | C2 | semidirect |
| 51. C2×#11924003 | D4 | semidirect |
| 190. #1387 | D73 | semidirect |
| 191. C73 | #13385 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22619603 | 2 |
| C2×#17988414 | 2 |
| C2×#17988393 | 2 |
| #22611644 | 2 |
| C2×#17988372 | 2 |
| #22609992 | 2 |
| C73×#1387 | 2 |
| #13385 | 73 |