Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
324 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 67 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. C2×#17985836 | C2 | semidirect |
| 3. #22586517 | C2 | semidirect |
| 4. C22⋊(C71⋊C32) | C2 | semidirect |
| 5. C71×#2216 | C2 | semidirect |
| 11. C2×C71⋊C32 | C22 | semidirect |
| 12. C2×Q32×C71 | C22 | semidirect |
| 15. #366×C71 | C22 | semidirect |
| 77. C22×C71 | SD64 | semidirect |
| 96. #2216 | D71 | semidirect |
| 99. C71 | #13664 | semidirect |
| 101. C2×Q32 | C2×D71 | semidirect |
| 109. #366 | C2×D71 | semidirect |
| 175. C22 | #17985836 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1136 | 2 |
| C2×#17985836 | 2 |
| #22586517 | 2 |
| C22⋊(C71⋊C32) | 2 |
| C71×#2216 | 2 |
| #13664 | 71 |