Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
308 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 1. #22590583 | C2 | semidirect |
| 3. #22587824 | C2 | semidirect |
| 4. #22586392 | C2 | semidirect |
| 5. #22586322 | C2 | semidirect |
| 6. #22586307 | C2 | semidirect |
| 7. C71×#3389 | C2 | semidirect |
| 78. D8×C71 | SD16 | semidirect |
| 146. #3389 | D71 | semidirect |
| 153. C71 | #12360 | semidirect |
| 221. D8 | #11765852 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590583 | 2 |
| #22590375 | 2 |
| #22587824 | 2 |
| #22586392 | 2 |
| #22586322 | 2 |
| #22586307 | 2 |
| C71×#3389 | 2 |
| #12360 | 71 |