Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
604 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 604 conjugacy classes of subgroups — too many to draw. Only its 85 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. #22616948 | C2 | semidirect |
| 2. #22611166 | C2 | semidirect |
| 3. #22611021 | C2 | semidirect |
| 5. #22607756 | C2 | semidirect |
| 6. #22607755 | C2 | semidirect |
| 7. C73×#1270 | C2 | semidirect |
| 71. C2×Dic146 | D8 | semidirect |
| 118. C2×D4×C73 | SD16 | semidirect |
| 245. #1270 | D73 | semidirect |
| 246. C73 | #7735 | semidirect |
| 333. C2×D4 | #11924017 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22616948 | 2 |
| #22611166 | 2 |
| #22611021 | 2 |
| #22611001 | 2 |
| #22607756 | 2 |
| #22607755 | 2 |
| C73×#1270 | 2 |
| #7735 | 73 |