Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
194 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 63 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. #22590227 | C2 | semidirect |
| 3. #22590217 | C2 | semidirect |
| 4. #22586546 | C2 | semidirect |
| 5. #22586531 | C2 | semidirect |
| 6. #22586528 | C2 | semidirect |
| 7. C71×#1398 | C2 | semidirect |
| 12. #17985838 | C4 | semidirect |
| 13. D2272 | C4 | semidirect |
| 25. Dic568 | C2×C4 | semidirect |
| 29. D1136 | C2×C4 | semidirect |
| 38. C32×C71 | C2×C4 | semidirect |
| 94. #1398 | D71 | semidirect |
| 95. C71 | #13658 | semidirect |
| 126. C32 | C4×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590655 | 2 |
| #22590227 | 2 |
| #22590217 | 2 |
| #22586546 | 2 |
| #22586531 | 2 |
| #22586528 | 2 |
| C71×#1398 | 2 |
| #13658 | 71 |