Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1092 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 1092 conjugacy classes of subgroups — too many to draw. Only its 147 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. #22589181 | C2 | semidirect |
| 2. #22587075 | C2 | semidirect |
| 3. #22586932 | C2 | semidirect |
| 4. #22586779 | C2 | semidirect |
| 6. #17986023 | C22 | semidirect |
| 8. C4×#11765849 | C22 | semidirect |
| 134. Q8×C71 | #100 | semidirect |
| 150. D4×C71 | #100 | semidirect |
| 202. C71 | #8469 | semidirect |
| 331. Q8 | #14556045 | semidirect |
| 347. D4 | #14556045 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22589181 | 2 |
| #22587075 | 2 |
| #22586932 | 2 |
| #22586779 | 2 |
| C71×#3498 | 2 |
| #8469 | 71 |