Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1154 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 1154 conjugacy classes of subgroups — too many to draw. Only its 187 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. #22598372 | C2 | semidirect |
| 3. #22593702 | C2 | semidirect |
| 4. #22587379 | C2 | semidirect |
| 5. #22587311 | C2 | semidirect |
| 6. #22586901 | C2 | semidirect |
| 7. C71×#1461 | C2 | semidirect |
| 118. C2×Q8×C71 | SD16 | semidirect |
| 201. #1461 | D71 | semidirect |
| 202. C71 | #18219 | semidirect |
| 289. C2×Q8 | #11765854 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22602111 | 2 |
| #22598372 | 2 |
| #22593702 | 2 |
| #22587379 | 2 |
| #22587311 | 2 |
| #22586901 | 2 |
| C71×#1461 | 2 |
| #18219 | 71 |