Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
594 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 129 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. C2×#17985803 | C2 | semidirect |
| 4. #22586418 | C2 | semidirect |
| 5. C2×#494×C71 | C2 | semidirect |
| 103. C2×C4×C71 | SD32 | semidirect |
| 144. C2×#494 | D71 | semidirect |
| 148. C71 | #13327 | semidirect |
| 252. C2×C4 | #14556071 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556071 | 2 |
| C2×#17985803 | 2 |
| #22589206 | 2 |
| #22586418 | 2 |
| C2×#494×C71 | 2 |
| #13327 | 71 |