Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
984 conjugacy classes of subgroups; only the 335 normal subgroups are shown.
This group has 984 conjugacy classes of subgroups — too many to draw. Only its 335 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. #22588633 | C2 | semidirect |
| 2. #22588483 | C2 | semidirect |
| 17. #127×C71 | C8 | semidirect |
| 30. C2×D4×C71 | C2×C8 | semidirect |
| 41. C42×C71 | C2×C8 | semidirect |
| 75. C71 | #23355 | semidirect |
| 88. #127 | C71⋊C8 | semidirect |
| 100. C2×D4 | C2×C71⋊C8 | semidirect |
| 113. C42 | C2×C71⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22588633 | 2 |
| #22588483 | 2 |
| C4×#127×C71 | 2 |
| #23355 | 71 |