Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
554 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 101 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. #22586769 | C2 | semidirect |
| 5. #22586735 | C2 | semidirect |
| 6. #22586198 | C2 | semidirect |
| 7. C71×#2581 | C2 | semidirect |
| 114. C2×Q8×C71 | SD16 | semidirect |
| 222. #2581 | D71 | semidirect |
| 227. C71 | #9999 | semidirect |
| 317. C2×Q8 | #11765852 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598371 | 2 |
| #22597812 | 2 |
| #22586899 | 2 |
| #22586769 | 2 |
| #22586735 | 2 |
| #22586198 | 2 |
| C71×#2581 | 2 |
| #9999 | 71 |