Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
642 conjugacy classes of subgroups; only the 199 normal subgroups are shown.
This group has 642 conjugacy classes of subgroups — too many to draw. Only its 199 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 |
|---|---|---|
| 2. #22589300 | C2 | semidirect |
| 4. C2×C8×C71⋊C8 | C2 | semidirect |
| 5. C71×#1844 | C2 | semidirect |
| 10. #17986372 | C4 | semidirect |
| 60. C2×C71⋊C8 | SD16 | semidirect |
| 101. C8×C71 | #102 | semidirect |
| 129. #1844 | D71 | semidirect |
| 131. C71 | #9820 | semidirect |
| 228. C8 | #14556048 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986372 | 2 |
| #22589300 | 2 |
| #22589145 | 2 |
| C2×C8×C71⋊C8 | 2 |
| C71×#1844 | 2 |
| #9820 | 71 |