Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
252 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 71 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. #22612188 | C2 | semidirect |
| 2. D4×#11924003 | C2 | semidirect |
| 4. #22608004 | C2 | semidirect |
| 5. #22607980 | C2 | semidirect |
| 6. #22607976 | C2 | semidirect |
| 7. C73×#1669 | C2 | semidirect |
| 56. #11924003 | D8 | semidirect |
| 79. D4×C73 | SD32 | semidirect |
| 120. #1669 | D73 | semidirect |
| 125. C73 | #12432 | semidirect |
| 202. D4 | #14556534 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22612188 | 2 |
| D4×#11924003 | 2 |
| #22609286 | 2 |
| #22608004 | 2 |
| #22607980 | 2 |
| #22607976 | 2 |
| C73×#1669 | 2 |
| #12432 | 73 |