Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
516 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 109 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. #22596928 | C2 | semidirect |
| 3. #22590077 | C2 | semidirect |
| 4. #22590075 | C2 | semidirect |
| 5. C2×#17985780 | C2 | semidirect |
| 6. #22586441 | C2 | semidirect |
| 7. C71×#1384 | C2 | semidirect |
| 13. #17986258 | C4 | semidirect |
| 14. #17986253 | C4 | semidirect |
| 33. C2×Dic284 | C2×C4 | semidirect |
| 35. C2×D568 | C2×C4 | semidirect |
| 60. #14556060 | D4 | semidirect |
| 72. #106×C71 | C2×C4 | semidirect |
| 73. #106×C71 | D4 | semidirect |
| 199. #1384 | D71 | semidirect |
| 200. C71 | #13008 | semidirect |
| 263. #106 | C4×D71 | semidirect |
| 264. #106 | D284 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597950 | 2 |
| #22596928 | 2 |
| #22590077 | 2 |
| #22590075 | 2 |
| C2×#17985780 | 2 |
| #22586441 | 2 |
| C71×#1384 | 2 |
| #13008 | 71 |