Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
706 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 706 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 |
|---|---|---|
| 1. #22618971 | C2 | semidirect |
| 3. #22609920 | C2 | semidirect |
| 4. #22608600 | C2 | semidirect |
| 5. #22608598 | C2 | semidirect |
| 6. #22607834 | C2 | semidirect |
| 7. C73×#1303 | C2 | semidirect |
| 50. C4⋊#10596831 | D4 | semidirect |
| 61. C4⋊C8×C73 | D4 | semidirect |
| 203. #1303 | D73 | semidirect |
| 204. C73 | #9405 | semidirect |
| 254. C4⋊C8 | D292 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22618971 | 2 |
| #22614873 | 2 |
| #22609920 | 2 |
| #22608600 | 2 |
| #22608598 | 2 |
| #22607834 | 2 |
| C73×#1303 | 2 |
| #9405 | 73 |