Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
150 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 43 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. #22586480 | C2 | semidirect |
| 2. #22586442 | C2 | semidirect |
| 6. C2×D16×C71 | C4 | semidirect |
| 9. #367×C71 | C4 | semidirect |
| 73. C71 | #7422 | semidirect |
| 74. C2×D16 | Dic71 | semidirect |
| 79. #367 | Dic71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22586480 | 2 |
| #22586442 | 2 |
| C71×#2218 | 2 |
| #7422 | 71 |