Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
294 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 4. #22586402 | C2 | semidirect |
| 5. #22586401 | C2 | semidirect |
| 6. #22586400 | C2 | semidirect |
| 7. C71×#1366 | C2 | semidirect |
| 118. D71 | #1366 | direct (N × H) |
| 125. #1366 | D71 | direct (N × H) |
| 126. C71 | C2×#1366 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #499×D71 | 2 |
| #364×D71 | 2 |
| #22586402 | 2 |
| #22586401 | 2 |
| #22586400 | 2 |
| C71×#1366 | 2 |
| C2×#1366 | 71 |