Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
422 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 107 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. #22590129 | C2 | semidirect |
| 5. #22589084 | C2 | semidirect |
| 6. #22586423 | C2 | semidirect |
| 7. C71×#1386 | C2 | semidirect |
| 21. #17985808 | C4 | semidirect |
| 49. #14556068 | C2×C4 | semidirect |
| 70. #106×C71 | C2×C4 | semidirect |
| 85. Dic284 | C4⋊C4 | semidirect |
| 89. D568 | C4⋊C4 | semidirect |
| 187. #1386 | D71 | semidirect |
| 189. C71 | #12943 | semidirect |
| 245. #106 | C4×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597140 | 2 |
| #22590129 | 2 |
| C2×#17985808 | 2 |
| #22590053 | 2 |
| #22589084 | 2 |
| #22586423 | 2 |
| C71×#1386 | 2 |
| #12943 | 71 |