Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
522 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 107 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. #22618731 | C2 | semidirect |
| 3. C2×#17988398 | C2 | semidirect |
| 4. #22610808 | C2 | semidirect |
| 5. #22608036 | C2 | semidirect |
| 6. #22608014 | C2 | semidirect |
| 7. C73×#2140 | C2 | semidirect |
| 11. #17989023 | C4 | semidirect |
| 48. #14556531 | C2×C4 | semidirect |
| 63. C2×D8×C73 | C2×C4 | semidirect |
| 83. Dic292 | C22⋊C4 | semidirect |
| 87. D584 | C22⋊C4 | semidirect |
| 188. #2140 | 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 |
| #22618731 | 2 |
| C2×#17988398 | 2 |
| #22610808 | 2 |
| #22608036 | 2 |
| #22608014 | 2 |
| C73×#2140 | 2 |
| #13025 | 73 |