Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
798 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 798 conjugacy classes of subgroups — too many to draw. Only its 211 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. #22598900 | C2 | semidirect |
| 3. #22587974 | C2 | semidirect |
| 4. #22587969 | C2 | semidirect |
| 5. #22587963 | C2 | semidirect |
| 6. C2×#17985720 | C2 | semidirect |
| 7. C71×#3160 | C2 | semidirect |
| 75. C2×C8×C71 | SD16 | semidirect |
| 122. #3160 | D71 | semidirect |
| 128. C71 | #19608 | semidirect |
| 194. C2×C8 | #11765852 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598900 | 2 |
| #22598768 | 2 |
| #22587974 | 2 |
| #22587969 | 2 |
| #22587963 | 2 |
| C2×#17985720 | 2 |
| C71×#3160 | 2 |
| #19608 | 71 |