Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
594 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 101 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×#17989023 | C2 | semidirect |
| 2. #22620374 | C2 | semidirect |
| 3. C2×#17988398 | C2 | semidirect |
| 4. C2×#17988397 | C2 | semidirect |
| 5. #22610808 | C2 | semidirect |
| 6. #22608014 | C2 | semidirect |
| 7. C2×#509×C73 | C2 | semidirect |
| 60. #14556531 | D4 | semidirect |
| 81. C2×D8×C73 | D4 | semidirect |
| 86. M32×C73 | D4 | semidirect |
| 230. C2×#509 | D73 | semidirect |
| 236. C73 | #13341 | semidirect |
| 290. C2×D8 | C22⋊D73 | semidirect |
| 309. M32 | C22⋊D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989023 | 2 |
| #22620374 | 2 |
| C2×#17988398 | 2 |
| C2×#17988397 | 2 |
| #22610808 | 2 |
| #22608014 | 2 |
| C2×#509×C73 | 2 |
| #13341 | 73 |