Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
564 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 564 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. #22596928 | C2 | semidirect |
| 3. #22590057 | C2 | semidirect |
| 4. #22590055 | C2 | semidirect |
| 5. C2×#17985780 | C2 | semidirect |
| 6. #22586447 | C2 | semidirect |
| 7. C71×#1386 | C2 | semidirect |
| 14. #17986253 | C4 | semidirect |
| 34. C2×D568 | C2×C4 | semidirect |
| 55. #14556062 | D4 | semidirect |
| 66. #107×C71 | D4 | semidirect |
| 69. #106×C71 | C2×C4 | semidirect |
| 193. #1386 | D71 | semidirect |
| 194. C71 | #12999 | semidirect |
| 250. #107 | D284 | semidirect |
| 255. #106 | C4×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986253 | 2 |
| #22596928 | 2 |
| #22590057 | 2 |
| #22590055 | 2 |
| C2×#17985780 | 2 |
| #22586447 | 2 |
| C71×#1386 | 2 |
| #12999 | 71 |