Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
662 conjugacy classes of subgroups; only the 270 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 270 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. #22626310 | C2 | semidirect |
| 2. #22626288 | C2 | semidirect |
| 3. #22626156 | C2 | semidirect |
| 5. C2×#14556664 | C22 | semidirect |
| 6. C4⋊#11924031 | C22 | semidirect |
| 7. #17989482 | C22 | semidirect |
| 9. C4×#11924031 | C22 | semidirect |
| 38. C2×D292 | C16 | semidirect |
| 64. C22×D73 | C2×C16 | semidirect |
| 69. C2×C4×C73 | C2×C16 | semidirect |
| 76. D292 | C2×C16 | semidirect |
| 108. C73 | #33486 | semidirect |
| 179. C2×C4 | #14556664 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626310 | 2 |
| #22626288 | 2 |
| #22626156 | 2 |
| C2×#17988652 | 2 |
| #33486 | 73 |