Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
770 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 770 conjugacy classes of subgroups — too many to draw. Only its 83 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. #22620920 | C2 | semidirect |
| 2. #22620381 | C2 | semidirect |
| 3. #22616038 | C2 | semidirect |
| 4. #22608530 | C2 | semidirect |
| 5. #22608440 | C2 | semidirect |
| 6. #22607823 | C2 | semidirect |
| 7. C73×#1555 | C2 | semidirect |
| 41. #14556591 | D4 | semidirect |
| 42. #14556588 | D4 | semidirect |
| 60. #14556502 | D4 | semidirect |
| 73. C4⋊C8×C73 | D4 | semidirect |
| 215. #1555 | D73 | semidirect |
| 219. C73 | #10088 | semidirect |
| 279. C4⋊C8 | C22⋊D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620920 | 2 |
| #22620381 | 2 |
| #22616038 | 2 |
| #22608530 | 2 |
| #22608440 | 2 |
| #22607823 | 2 |
| C73×#1555 | 2 |
| #10088 | 73 |