Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
212 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 4. #22586412 | C2 | semidirect |
| 5. #22586398 | C2 | semidirect |
| 6. #22586395 | C2 | semidirect |
| 7. C71×#2254 | C2 | semidirect |
| 65. C16×C71 | SD16 | semidirect |
| 103. #2254 | D71 | semidirect |
| 110. C71 | #12456 | semidirect |
| 168. C16 | #11765852 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590173 | 2 |
| #22587736 | 2 |
| #22587726 | 2 |
| #22586412 | 2 |
| #22586398 | 2 |
| #22586395 | 2 |
| C71×#2254 | 2 |
| #12456 | 71 |