Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
626 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 626 conjugacy classes of subgroups — too many to draw. Only its 112 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. C22×#14556660 | C2 | semidirect |
| 2. C2×#17989499 | C2 | semidirect |
| 3. #22626156 | C2 | semidirect |
| 4. #22624988 | C2 | semidirect |
| 17. #17988824 | C4 | semidirect |
| 18. #17988823 | C4 | semidirect |
| 21. #17988820 | C4 | semidirect |
| 24. #466×C73 | C4 | semidirect |
| 35. #14556660 | D4 | semidirect |
| 39. C2×D584 | C2×C4 | semidirect |
| 57. #14556525 | C2×C4 | semidirect |
| 62. C2×D8×C73 | C2×C4 | semidirect |
| 65. #107×C73 | C2×C4 | semidirect |
| 185. C22×C73 | #357 | semidirect |
| 200. C2×D73 | #357 | semidirect |
| 233. C73 | #12991 | semidirect |
| 244. #466 | #64408 | semidirect |
| 261. C2×D8 | C2×#64408 | semidirect |
| 290. #107 | C2×#64408 | semidirect |
| 433. C22 | #17989499 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556660 | 2 |
| C2×#17989499 | 2 |
| #22626156 | 2 |
| #22624988 | 2 |
| #466×D73 | 2 |
| #12991 | 73 |