Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
814 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 814 conjugacy classes of subgroups — too many to draw. Only its 219 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. #22587942 | C2 | semidirect |
| 4. #22587938 | C2 | semidirect |
| 5. #22587933 | C2 | semidirect |
| 6. #22587928 | C2 | semidirect |
| 7. C2×C8×C71⋊C8 | C2 | semidirect |
| 8. C71×#3160 | C2 | semidirect |
| 79. C2×C8×C71 | SD16 | semidirect |
| 109. C71⋊C8 | #135 | semidirect |
| 127. #3160 | D71 | semidirect |
| 134. C71 | #19596 | semidirect |
| 203. 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 |
| #22587942 | 2 |
| #22587938 | 2 |
| #22587933 | 2 |
| #22587928 | 2 |
| C2×C8×C71⋊C8 | 2 |
| C71×#3160 | 2 |
| #19596 | 71 |