Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
554 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22593702 | C2 | semidirect |
| 5. #22586770 | C2 | semidirect |
| 6. #22586199 | C2 | semidirect |
| 7. C71×#1479 | C2 | semidirect |
| 124. C2×Q8×C71 | SD16 | semidirect |
| 225. #1479 | D71 | semidirect |
| 227. C71 | #9999 | semidirect |
| 317. C2×Q8 | #11765854 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598372 | 2 |
| #22597812 | 2 |
| #22593702 | 2 |
| #22586901 | 2 |
| #22586770 | 2 |
| #22586199 | 2 |
| C71×#1479 | 2 |
| #9999 | 71 |