Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1546 conjugacy classes of subgroups; only the 355 normal subgroups are shown.
This group has 1546 conjugacy classes of subgroups — too many to draw. Only its 355 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. #22588412 | C2 | semidirect |
| 4. #22588072 | C2 | semidirect |
| 8. C2×D4×Dic71 | C4 | semidirect |
| 135. C71 | #20690 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986474 | 2 |
| #22590922 | 2 |
| #22588412 | 2 |
| #22588072 | 2 |
| C71×#2309 | 2 |
| #20690 | 71 |