Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
224 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 75 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. #22587237 | C2 | semidirect |
| 4. #22586413 | C2 | semidirect |
| 6. C16×C71⋊C8 | C2 | semidirect |
| 7. C71×#1332 | C2 | semidirect |
| 56. C71⋊C16 | M16 | semidirect |
| 88. C71⋊C8 | SD32 | semidirect |
| 110. #1332 | D71 | semidirect |
| 113. C71 | #12082 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14556071 | 2 |
| #22587237 | 2 |
| #22587224 | 2 |
| #22586413 | 2 |
| #22586302 | 2 |
| C16×C71⋊C8 | 2 |
| C71×#1332 | 2 |
| #12082 | 71 |