Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
840 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 840 conjugacy classes of subgroups — too many to draw. Only its 115 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. #22612284 | C2 | semidirect |
| 2. #22608447 | C2 | semidirect |
| 3. #22608258 | C2 | semidirect |
| 4. #22607817 | C2 | semidirect |
| 17. #399×C73 | C4 | semidirect |
| 18. #392×C73 | C4 | semidirect |
| 31. #14556498 | D4 | semidirect |
| 35. C22×D4×C73 | C2×C4 | semidirect |
| 43. C2×C4⋊C4×C73 | C2×C4 | semidirect |
| 53. #95×C73 | C2×C4 | semidirect |
| 194. C73 | #9409 | semidirect |
| 201. #399 | Dic73 | semidirect |
| 202. #392 | Dic73 | semidirect |
| 213. C22×D4 | C2×Dic73 | semidirect |
| 223. C2×C4⋊C4 | C2×Dic73 | semidirect |
| 242. #95 | C2×Dic73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22612284 | 2 |
| #22608447 | 2 |
| #22608258 | 2 |
| #22607817 | 2 |
| C73×#2539 | 2 |
| #9409 | 73 |