Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
684 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 83 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. #22599343 | C2 | semidirect |
| 2. #22598715 | C2 | semidirect |
| 4. #22587053 | C2 | semidirect |
| 5. #22586853 | C2 | semidirect |
| 6. #22586234 | C2 | semidirect |
| 7. C71×#1527 | C2 | semidirect |
| 37. #14556128 | D4 | semidirect |
| 38. #14556128 | D4 | semidirect |
| 53. C4⋊(C71⋊C8) | D4 | semidirect |
| 75. #97×C71 | D4 | semidirect |
| 205. #1527 | D71 | semidirect |
| 208. C71 | #10096 | semidirect |
| 274. #97 | C22⋊D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599343 | 2 |
| #22598715 | 2 |
| #22594448 | 2 |
| #22587053 | 2 |
| #22586853 | 2 |
| #22586234 | 2 |
| C71×#1527 | 2 |
| #10096 | 71 |