Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1030 conjugacy classes of subgroups; only the 267 normal subgroups are shown.
This group has 1030 conjugacy classes of subgroups — too many to draw. Only its 267 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×#17986397 | C2 | semidirect |
| 3. C2×#17986372 | C2 | semidirect |
| 4. C2×#17986346 | C2 | semidirect |
| 5. #22587968 | C2 | direct (N × H) |
| 6. C2×#322×C71 | C2 | semidirect |
| 13. #17986397 | C22 | semidirect |
| 17. #17986372 | C22 | semidirect |
| 19. #17986346 | C22 | semidirect |
| 24. #322×C71 | C22 | semidirect |
| 82. C2×C8×C71 | SD16 | semidirect |
| 114. C8×C71 | C2×SD16 | semidirect |
| 130. C2×C71 | #1715 | semidirect |
| 140. C2×#322 | D71 | semidirect |
| 141. C71 | C2×#1715 | semidirect |
| 159. #322 | C2×D71 | semidirect |
| 213. C2×C8 | #11765854 | semidirect |
| 249. C8 | C2×#11765854 | semidirect |
| 266. C2 | #22587968 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986397 | 2 |
| C2×#17986376 | 2 |
| C2×#17986372 | 2 |
| C2×#17986346 | 2 |
| #22587968 | 2 |
| C2×#322×C71 | 2 |
| C2×#1715 | 71 |