Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
950 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 950 conjugacy classes of subgroups — too many to draw. Only its 107 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. #22599260 | C2 | semidirect |
| 2. #22599258 | C2 | semidirect |
| 3. #22596734 | C2 | semidirect |
| 4. #22589167 | C2 | semidirect |
| 5. #22587009 | C2 | semidirect |
| 6. #22586172 | C2 | semidirect |
| 7. C71×#1545 | C2 | semidirect |
| 36. #14556128 | D4 | semidirect |
| 41. #14556125 | D4 | semidirect |
| 54. C4⋊(C71⋊C8) | D4 | semidirect |
| 71. C4⋊C8×C71 | D4 | semidirect |
| 107. C4×Dic71 | D8 | semidirect |
| 215. #1545 | D71 | semidirect |
| 217. C71 | #10280 | semidirect |
| 276. C4⋊C8 | C22⋊D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599260 | 2 |
| #22599258 | 2 |
| #22596734 | 2 |
| #22589167 | 2 |
| #22587009 | 2 |
| #22586172 | 2 |
| C71×#1545 | 2 |
| #10280 | 71 |