Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1146 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 1146 conjugacy classes of subgroups — too many to draw. Only its 251 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. C2×#17986375 | C2 | semidirect |
| 2. C2×#17986372 | C2 | semidirect |
| 3. C2×#17986345 | C2 | semidirect |
| 4. #22588007 | C2 | direct (N × H) |
| 5. C2×#17985720 | C2 | semidirect |
| 6. C2×#493×C71 | C2 | semidirect |
| 12. #17986375 | C22 | semidirect |
| 14. #17986372 | C22 | semidirect |
| 16. #17986345 | C22 | semidirect |
| 19. #17985720 | C22 | semidirect |
| 23. #493×C71 | C22 | semidirect |
| 86. C2×C8×C71 | D8 | semidirect |
| 119. C8×C71 | C2×D8 | semidirect |
| 138. C2×C71 | #1721 | semidirect |
| 143. C2×#493 | D71 | semidirect |
| 148. C71 | C2×#1721 | semidirect |
| 158. #493 | C2×D71 | semidirect |
| 226. C2×C8 | #11765850 | semidirect |
| 262. C8 | C2×#11765850 | semidirect |
| 280. C2 | #22588007 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986375 | 2 |
| C2×#17986372 | 2 |
| C2×#17986345 | 2 |
| #22588007 | 2 |
| C2×#17985720 | 2 |
| C2×#493×C71 | 2 |
| C2×#1721 | 71 |