Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
402 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 2. C2×#17985827 | C2 | semidirect |
| 5. #22589125 | C2 | semidirect |
| 6. #22586449 | C2 | semidirect |
| 7. C71×#1379 | C2 | semidirect |
| 19. #17985807 | C4 | semidirect |
| 43. #14556064 | C2×C4 | semidirect |
| 60. C2×C16×C71 | C2×C4 | semidirect |
| 166. #1379 | D71 | semidirect |
| 167. C71 | #12946 | semidirect |
| 210. C2×C16 | C4×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597217 | 2 |
| C2×#17985827 | 2 |
| C2×#17985807 | 2 |
| #22590053 | 2 |
| #22589125 | 2 |
| #22586449 | 2 |
| C71×#1379 | 2 |
| #12946 | 71 |