Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
240 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 240 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. #22587224 | C2 | semidirect |
| 3. D8×C71⋊C8 | C2 | semidirect |
| 4. #22586413 | C2 | semidirect |
| 5. #22586302 | C2 | semidirect |
| 6. #22586259 | C2 | semidirect |
| 7. C71×#1331 | C2 | semidirect |
| 61. D8×C71 | M16 | semidirect |
| 117. #1331 | D71 | semidirect |
| 119. C71 | #12073 | semidirect |
| 163. D8 | #11765848 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14556069 | 2 |
| #22587224 | 2 |
| D8×C71⋊C8 | 2 |
| #22586413 | 2 |
| #22586302 | 2 |
| #22586259 | 2 |
| C71×#1331 | 2 |
| #12073 | 71 |