Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
586 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 586 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. C22×#14556532 | C2 | semidirect |
| 2. #22620418 | C2 | semidirect |
| 3. C2×#17988401 | C2 | semidirect |
| 4. C2×#17988394 | C2 | semidirect |
| 5. #22610842 | C2 | semidirect |
| 6. #22608021 | C2 | semidirect |
| 7. C2×#509×C73 | C2 | semidirect |
| 52. C2×#11924003 | D4 | semidirect |
| 73. C2×D8×C73 | D4 | semidirect |
| 78. M32×C73 | D4 | semidirect |
| 207. C2×#509 | D73 | semidirect |
| 214. C73 | #13336 | semidirect |
| 263. C2×D8 | C22⋊D73 | semidirect |
| 276. M32 | C22⋊D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556532 | 2 |
| #22620418 | 2 |
| C2×#17988401 | 2 |
| C2×#17988394 | 2 |
| #22610842 | 2 |
| #22608021 | 2 |
| C2×#509×C73 | 2 |
| #13336 | 73 |