Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
522 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 522 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. #22618733 | C2 | semidirect |
| 3. C2×#17988396 | C2 | semidirect |
| 4. #22611647 | C2 | semidirect |
| 5. #22608038 | C2 | semidirect |
| 6. #22608015 | C2 | semidirect |
| 7. C73×#1972 | C2 | semidirect |
| 11. #17989023 | C4 | semidirect |
| 47. #14556531 | C2×C4 | semidirect |
| 60. C2×D8×C73 | C2×C4 | semidirect |
| 81. Dic292 | C22⋊C4 | semidirect |
| 85. D584 | C22⋊C4 | semidirect |
| 189. #1972 | D73 | semidirect |
| 192. C73 | #13025 | semidirect |
| 227. C2×D8 | C4×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989023 | 2 |
| #22618733 | 2 |
| C2×#17988396 | 2 |
| #22611647 | 2 |
| #22608038 | 2 |
| #22608015 | 2 |
| C73×#1972 | 2 |
| #13025 | 73 |