Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
568 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 101 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. #22623067 | C2 | semidirect |
| 2. C2×#17989025 | C2 | semidirect |
| 3. #22620417 | C2 | semidirect |
| 4. #22611668 | C2 | semidirect |
| 5. #22611648 | C2 | semidirect |
| 6. #22610829 | C2 | semidirect |
| 7. C73×#1378 | C2 | semidirect |
| 47. C2×Dic292 | D4 | semidirect |
| 59. C2×D584 | D4 | semidirect |
| 81. M32×C73 | D4 | semidirect |
| 83. C2×C16×C73 | D4 | semidirect |
| 224. #1378 | D73 | semidirect |
| 225. C73 | #13334 | semidirect |
| 295. M32 | D292 | semidirect |
| 297. C2×C16 | D292 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22623067 | 2 |
| C2×#17989025 | 2 |
| #22620417 | 2 |
| #22611668 | 2 |
| #22611648 | 2 |
| #22610829 | 2 |
| C73×#1378 | 2 |
| #13334 | 73 |