Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
294 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 61 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 |
|---|---|---|
| 1. C2×Q32×D71 | C2 | semidirect |
| 2. C2×#17985838 | C2 | semidirect |
| 3. C2×#17985836 | C2 | semidirect |
| 5. #22586520 | C2 | semidirect |
| 6. (C2×D71)⋊C32 | C2 | semidirect |
| 7. C71×#1416 | C2 | semidirect |
| 32. Dic568 | D4 | semidirect |
| 43. Q32×C71 | D4 | semidirect |
| 99. C2×D71 | SD64 | semidirect |
| 117. #1416 | D71 | semidirect |
| 119. C71 | #13662 | semidirect |
| 148. Q32 | D284 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q32×D71 | 2 |
| C2×#17985838 | 2 |
| C2×#17985836 | 2 |
| #22590427 | 2 |
| #22586520 | 2 |
| (C2×D71)⋊C32 | 2 |
| C71×#1416 | 2 |
| #13662 | 71 |