Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
538 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 538 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. C2×#17988700 | C2 | semidirect |
| 3. C2×#17988401 | C2 | semidirect |
| 4. C2×#17988398 | C2 | semidirect |
| 5. #22610824 | C2 | semidirect |
| 6. #22608030 | C2 | semidirect |
| 7. C73×#1375 | C2 | semidirect |
| 13. C2×#14556536 | C4 | semidirect |
| 14. C2×D1168 | C4 | semidirect |
| 34. C2×Dic292 | C2×C4 | semidirect |
| 40. C2×D584 | C2×C4 | semidirect |
| 65. C2×C16×C73 | C2×C4 | semidirect |
| 185. #1375 | D73 | semidirect |
| 186. C73 | #13037 | semidirect |
| 237. C2×C16 | C4×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989025 | 2 |
| C2×#17988700 | 2 |
| C2×#17988401 | 2 |
| C2×#17988398 | 2 |
| #22610824 | 2 |
| #22608030 | 2 |
| C73×#1375 | 2 |
| #13037 | 73 |