Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
442 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 73 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. #22590386 | C2 | semidirect |
| 4. #22587705 | C2 | semidirect |
| 5. #22586387 | C2 | semidirect |
| 6. #22586302 | C2 | semidirect |
| 7. C71×D4⋊C16 | C2 | semidirect |
| 12. #17986379 | C22 | semidirect |
| 20. #17985752 | C22 | semidirect |
| 23. C4⋊C16×C71 | C22 | semidirect |
| 24. C4×C16×C71 | C22 | semidirect |
| 103. D4×C71 | SD32 | semidirect |
| 162. D4⋊C16 | D71 | semidirect |
| 163. C71 | #12320 | semidirect |
| 176. C4⋊C16 | C2×D71 | semidirect |
| 178. C4×C16 | C2×D71 | semidirect |
| 270. D4 | #14556073 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×D568 | 2 |
| #22590596 | 2 |
| #22590386 | 2 |
| #22587705 | 2 |
| #22586387 | 2 |
| #22586302 | 2 |
| C71×D4⋊C16 | 2 |
| #12320 | 71 |