Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
442 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 442 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 |
|---|---|---|
| 2. #22590596 | C2 | semidirect |
| 3. #22590385 | C2 | semidirect |
| 4. #22587706 | C2 | semidirect |
| 5. #22586385 | C2 | semidirect |
| 6. #22586296 | C2 | semidirect |
| 7. C71×#1331 | C2 | semidirect |
| 12. #17986379 | C22 | semidirect |
| 19. C4⋊(C71⋊C16) | C22 | semidirect |
| 23. C4×C16×C71 | C22 | semidirect |
| 24. #335×C71 | C22 | semidirect |
| 120. D284 | SD32 | semidirect |
| 161. #1331 | D71 | semidirect |
| 163. C71 | #12320 | semidirect |
| 178. C4×C16 | C2×D71 | semidirect |
| 179. #335 | C2×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D8×D284 | 2 |
| #22590596 | 2 |
| #22590385 | 2 |
| #22587706 | 2 |
| #22586385 | 2 |
| #22586296 | 2 |
| C71×#1331 | 2 |
| #12320 | 71 |