Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
516 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 516 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. #22618519 | C2 | semidirect |
| 3. #22611668 | C2 | semidirect |
| 4. #22611666 | C2 | semidirect |
| 5. C2×#17988368 | C2 | semidirect |
| 6. #22608032 | C2 | semidirect |
| 7. C73×#1384 | C2 | semidirect |
| 13. #17988846 | C4 | semidirect |
| 14. #17988841 | C4 | semidirect |
| 33. C2×Dic292 | C2×C4 | semidirect |
| 35. C2×D584 | C2×C4 | semidirect |
| 60. #14556523 | D4 | semidirect |
| 72. #106×C73 | C2×C4 | semidirect |
| 73. #106×C73 | D4 | semidirect |
| 199. #1384 | D73 | semidirect |
| 200. C73 | #13008 | semidirect |
| 263. #106 | C4×D73 | semidirect |
| 264. #106 | D292 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22619541 | 2 |
| #22618519 | 2 |
| #22611668 | 2 |
| #22611666 | 2 |
| C2×#17988368 | 2 |
| #22608032 | 2 |
| C73×#1384 | 2 |
| #13008 | 73 |