Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
508 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 2. C2×#17986121 | C2 | semidirect |
| 3. C2×#17985813 | C2 | semidirect |
| 4. #22589214 | C2 | semidirect |
| 5. #22586438 | C2 | semidirect |
| 6. #22586419 | C2 | semidirect |
| 7. C2×#360×C71 | C2 | semidirect |
| 12. C2×#14556071 | C4 | semidirect |
| 13. C2×#14556069 | C4 | semidirect |
| 103. Q16×C71 | C22⋊C4 | semidirect |
| 107. D8×C71 | C22⋊C4 | semidirect |
| 181. C2×#360 | D71 | semidirect |
| 185. C71 | #13040 | semidirect |
| 265. Q16 | (C2×D71)⋊C4 | semidirect |
| 273. D8 | (C2×D71)⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986434 | 2 |
| C2×#17986121 | 2 |
| C2×#17985813 | 2 |
| #22589214 | 2 |
| #22586438 | 2 |
| #22586419 | 2 |
| C2×#360×C71 | 2 |
| #13040 | 71 |