Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
3590 conjugacy classes of subgroups; only the 907 normal subgroups are shown.
This group has 3590 conjugacy classes of subgroups — too many to draw. Only its 907 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. C22×#14556128 | C2 | semidirect |
| 3. #22594450 | C2 | direct (N × H) |
| 4. C2×#17985936 | C2 | semidirect |
| 5. C2×#376×C71 | C2 | semidirect |
| 9. C2×#14556128 | C22 | semidirect |
| 14. #17985936 | C22 | semidirect |
| 16. #376×C71 | C22 | semidirect |
| 84. C2×C71 | #2658 | semidirect |
| 92. C2×#376 | D71 | semidirect |
| 93. C71 | C2×#2658 | semidirect |
| 104. #376 | C2×D71 | semidirect |
| 172. C2 | #22594450 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556128 | 2 |
| C22×#14556116 | 2 |
| #22594450 | 2 |
| C2×#17985936 | 2 |
| C2×#376×C71 | 2 |
| C2×#2658 | 71 |