Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1078 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 1078 conjugacy classes of subgroups — too many to draw. Only its 219 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. C2×#17986368 | C2 | semidirect |
| 4. #22589492 | C2 | semidirect |
| 5. #22589309 | C2 | semidirect |
| 128. C22×C71 | #491 | semidirect |
| 155. C71 | #25912 | semidirect |
| 276. C22 | #17986368 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556120 | 2 |
| C2×#17986368 | 2 |
| #22596692 | 2 |
| #22589492 | 2 |
| #22589309 | 2 |
| #22588645 | 2 |
| C71×#1749 | 2 |
| #25912 | 71 |