Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
220 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 79 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. #22587238 | C2 | semidirect |
| 4. #22586412 | C2 | semidirect |
| 5. #22586305 | C2 | semidirect |
| 7. C71×#1311 | C2 | semidirect |
| 67. C16×C71 | M16 | semidirect |
| 112. #1311 | D71 | semidirect |
| 113. C71 | #12084 | semidirect |
| 173. C16 | #11765848 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14556073 | 2 |
| #22587238 | 2 |
| #22587226 | 2 |
| #22586412 | 2 |
| #22586305 | 2 |
| #22586302 | 2 |
| C71×#1311 | 2 |
| #12084 | 71 |