Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
3550 conjugacy classes of subgroups; only the 667 normal subgroups are shown.
This group has 3550 conjugacy classes of subgroups — too many to draw. Only its 667 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. #22596593 | C2 | direct (N × H) |
| 2. C2×#17985911 | C2 | semidirect |
| 5. C23×Dic142 | C22 | semidirect |
| 7. #17985911 | C22 | semidirect |
| 9. C2×C71⋊#95 | C22 | semidirect |
| 14. C22×Dic142 | C23 | semidirect |
| 18. C71⋊#95 | C23 | semidirect |
| 20. C25×C71 | Q8 | semidirect |
| 37. C24×C71 | C2×Q8 | semidirect |
| 73. C2×C71 | #2840 | semidirect |
| 80. C71 | C2×#2840 | semidirect |
| 90. C25 | Dic142 | semidirect |
| 108. C24 | C2×Dic142 | semidirect |
| 148. C2 | #22596593 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22596593 | 2 |
| C2×#17985911 | 2 |
| C2×#17985855 | 2 |
| C2×#379×C71 | 2 |
| C2×#2840 | 71 |