Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
252 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 63 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×#17985838 | C2 | semidirect |
| 2. C2×#17985837 | C2 | semidirect |
| 3. C2×#17985834 | C2 | semidirect |
| 4. #22590598 | C2 | semidirect |
| 5. #22590588 | C2 | semidirect |
| 6. #22586473 | C2 | semidirect |
| 7. C2×D32×C71 | C2 | semidirect |
| 37. C71⋊C32 | D4 | semidirect |
| 45. C32×C71 | D4 | semidirect |
| 106. C2×D32 | D71 | semidirect |
| 110. C71 | #13729 | semidirect |
| 148. C32 | C22⋊D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985838 | 2 |
| C2×#17985837 | 2 |
| C2×#17985834 | 2 |
| #22590598 | 2 |
| #22590588 | 2 |
| #22586473 | 2 |
| C2×D32×C71 | 2 |
| #13729 | 71 |