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. #22620914 | C2 | semidirect |
| 2. #22620384 | C2 | semidirect |
| 3. #22616037 | C2 | semidirect |
| 4. #22608644 | C2 | semidirect |
| 5. #22608530 | C2 | semidirect |
| 6. #22607824 | C2 | semidirect |
| 7. C73×#1505 | C2 | semidirect |
| 56. C4⋊#10596831 | D4 | semidirect |
| 61. #14556502 | D4 | semidirect |
| 64. C4⋊Q8×C73 | D4 | semidirect |
| 65. #127×C73 | D4 | semidirect |
| 217. #1505 | D73 | semidirect |
| 219. C73 | #10088 | semidirect |
| 256. C4⋊Q8 | D292 | semidirect |
| 262. #127 | D292 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620914 | 2 |
| #22620384 | 2 |
| #22616037 | 2 |
| #22608644 | 2 |
| #22608530 | 2 |
| #22607824 | 2 |
| C73×#1505 | 2 |
| #10088 | 73 |