Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
440 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 95 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. #22589328 | C2 | semidirect |
| 3. #22589263 | C2 | semidirect |
| 5. #22587093 | C2 | semidirect |
| 7. C71×#1303 | C2 | semidirect |
| 89. #11765849 | SD16 | semidirect |
| 193. #1303 | D71 | semidirect |
| 194. C71 | #10501 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599267 | 2 |
| #22589328 | 2 |
| #22589263 | 2 |
| #22589258 | 2 |
| #22587093 | 2 |
| #22587018 | 2 |
| C71×#1303 | 2 |
| #10501 | 71 |