Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
798 conjugacy classes of subgroups; only the 227 normal subgroups are shown.
This group has 798 conjugacy classes of subgroups — too many to draw. Only its 227 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. #22598899 | C2 | semidirect |
| 2. #22598854 | C2 | semidirect |
| 4. #22587973 | C2 | semidirect |
| 5. #22587968 | C2 | semidirect |
| 6. #22587962 | C2 | semidirect |
| 7. C2×#322×C71 | C2 | semidirect |
| 79. C2×C8×C71 | SD16 | semidirect |
| 127. C2×#322 | D71 | semidirect |
| 128. C71 | #19608 | semidirect |
| 193. C2×C8 | #11765854 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598899 | 2 |
| #22598854 | 2 |
| #22598768 | 2 |
| #22587973 | 2 |
| #22587968 | 2 |
| #22587962 | 2 |
| C2×#322×C71 | 2 |
| #19608 | 71 |