Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
498 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 103 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. #22597191 | C2 | semidirect |
| 3. #22590057 | C2 | semidirect |
| 4. #22589239 | C2 | semidirect |
| 5. #22586441 | C2 | semidirect |
| 6. #22586427 | C2 | semidirect |
| 7. C71×#2145 | C2 | semidirect |
| 12. C2×#14556071 | C4 | semidirect |
| 13. C2×#14556069 | C4 | semidirect |
| 44. C2×C71⋊C16 | C2×C4 | semidirect |
| 57. C2×Q16×C71 | C2×C4 | semidirect |
| 59. C2×D8×C71 | C2×C4 | semidirect |
| 176. #2145 | D71 | semidirect |
| 181. C71 | #13033 | semidirect |
| 207. C2×Q16 | C4×D71 | semidirect |
| 215. C2×D8 | C4×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986434 | 2 |
| #22597191 | 2 |
| #22590057 | 2 |
| #22589239 | 2 |
| #22586441 | 2 |
| #22586427 | 2 |
| C71×#2145 | 2 |
| #13033 | 71 |