Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1162 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 1162 conjugacy classes of subgroups — too many to draw. Only its 171 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×#17985812 | C2 | semidirect |
| 2. #22589951 | C2 | semidirect |
| 3. #22588378 | C2 | semidirect |
| 5. C2×#14556068 | C22 | semidirect |
| 6. C2×#14556064 | C22 | semidirect |
| 115. C22×C71 | #361 | semidirect |
| 132. C71 | #12736 | semidirect |
| 243. C22 | #17985812 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985812 | 2 |
| #22589951 | 2 |
| #22588378 | 2 |
| C23×D8×C71 | 2 |
| #12736 | 71 |