Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
420 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22589317 | C2 | semidirect |
| 4. #22587028 | C2 | semidirect |
| 6. #22586215 | C2 | semidirect |
| 7. C71×#1831 | C2 | semidirect |
| 114. C42×C71 | SD16 | semidirect |
| 193. #1831 | D71 | semidirect |
| 197. C71 | #10521 | semidirect |
| 304. C42 | #11765854 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599657 | 2 |
| #22589317 | 2 |
| #22589168 | 2 |
| #22587028 | 2 |
| #22587015 | 2 |
| #22586215 | 2 |
| C71×#1831 | 2 |
| #10521 | 71 |