Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
950 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 950 conjugacy classes of subgroups — too many to draw. Only its 109 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. #22599255 | C2 | semidirect |
| 2. #22596734 | C2 | semidirect |
| 3. #22589169 | C2 | semidirect |
| 4. #22587008 | C2 | semidirect |
| 5. #22587007 | C2 | semidirect |
| 6. #22586172 | C2 | semidirect |
| 7. C71×#3205 | C2 | semidirect |
| 48. C4⋊(C71⋊C8) | D4 | semidirect |
| 58. C4⋊Q8×C71 | D4 | semidirect |
| 63. #127×C71 | D4 | semidirect |
| 70. C4⋊C8×C71 | D4 | semidirect |
| 96. C4×Dic71 | D8 | semidirect |
| 211. #3205 | D71 | semidirect |
| 217. C71 | #10280 | semidirect |
| 250. C4⋊Q8 | C22⋊D71 | semidirect |
| 263. #127 | C22⋊D71 | 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 |
|---|---|
| #22599255 | 2 |
| #22596734 | 2 |
| #22589169 | 2 |
| #22587008 | 2 |
| #22587007 | 2 |
| #22586172 | 2 |
| C71×#3205 | 2 |
| #10280 | 71 |