Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
552 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 97 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. C2×#17986435 | C2 | semidirect |
| 2. #22598060 | C2 | semidirect |
| 3. C2×#17985812 | C2 | semidirect |
| 4. #22590075 | C2 | semidirect |
| 5. #22589968 | C2 | semidirect |
| 6. #22586456 | C2 | semidirect |
| 7. C71×#3058 | C2 | semidirect |
| 41. C2×Dic284 | D4 | semidirect |
| 43. C2×D568 | D4 | semidirect |
| 50. #14556068 | D4 | semidirect |
| 54. #14556064 | D4 | semidirect |
| 214. #3058 | D71 | semidirect |
| 219. C71 | #13310 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986435 | 2 |
| #22598060 | 2 |
| C2×#17985812 | 2 |
| #22590075 | 2 |
| #22589968 | 2 |
| #22586456 | 2 |
| C71×#3058 | 2 |
| #13310 | 71 |