Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
428 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 3. #22588384 | C2 | semidirect |
| 4. #22586461 | C2 | semidirect |
| 5. C71×#1391 | C2 | semidirect |
| 6. C2×#14556136 | C4 | semidirect |
| 12. #17986022 | C4 | semidirect |
| 14. #17985965 | C4 | semidirect |
| 15. C2×C8×Dic71 | C4 | semidirect |
| 155. #1391 | D71 | semidirect |
| 156. C71 | #12807 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597048 | 2 |
| #22590003 | 2 |
| #22588384 | 2 |
| #22586461 | 2 |
| C71×#1391 | 2 |
| #12807 | 71 |