Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
516 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 127 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. #22611666 | C2 | semidirect |
| 3. C2×#17988369 | C2 | semidirect |
| 4. #22608032 | C2 | semidirect |
| 5. C73×#2911 | C2 | semidirect |
| 9. #17988845 | C4 | semidirect |
| 10. #17988840 | C4 | semidirect |
| 24. C2×Dic292 | C2×C4 | semidirect |
| 26. C2×D584 | C2×C4 | semidirect |
| 37. #14556523 | C2×C4 | semidirect |
| 57. #106×C73 | D4 | semidirect |
| 163. #2911 | D73 | semidirect |
| 167. C73 | #13008 | semidirect |
| 217. #106 | C22⋊D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22619540 | 2 |
| #22611666 | 2 |
| C2×#17988369 | 2 |
| #22608032 | 2 |
| C73×#2911 | 2 |
| #13008 | 73 |