Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
678 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 678 conjugacy classes of subgroups — too many to draw. Only its 105 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. #22598793 | C2 | semidirect |
| 3. #22589266 | C2 | semidirect |
| 4. #22589260 | C2 | semidirect |
| 5. #22586835 | C2 | semidirect |
| 6. #22586190 | C2 | semidirect |
| 7. C71×#3245 | C2 | semidirect |
| 96. #11765849 | D8 | semidirect |
| 221. #3245 | D71 | semidirect |
| 228. C71 | #10192 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599255 | 2 |
| #22598793 | 2 |
| #22589266 | 2 |
| #22589260 | 2 |
| #22586835 | 2 |
| #22586190 | 2 |
| C71×#3245 | 2 |
| #10192 | 71 |