Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
454 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 3. #22586243 | C2 | semidirect |
| 4. #22586169 | C2 | semidirect |
| 5. C71×#2399 | C2 | semidirect |
| 21. #14556128 | Q8 | semidirect |
| 22. #14556125 | Q8 | semidirect |
| 141. #2399 | D71 | semidirect |
| 146. C71 | #10370 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22589172 | 2 |
| #22586834 | 2 |
| #22586243 | 2 |
| #22586169 | 2 |
| C71×#2399 | 2 |
| #10370 | 71 |