Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
882 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 882 conjugacy classes of subgroups — too many to draw. Only its 187 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. #22587642 | C2 | direct (N × H) |
| 3. C2×#17985741 | C2 | semidirect |
| 4. C2×#564×C71 | C2 | semidirect |
| 10. #17985741 | C22 | semidirect |
| 12. #564×C71 | C22 | semidirect |
| 67. C2×C71 | #1658 | semidirect |
| 70. C2×#564 | D71 | semidirect |
| 74. C71 | C2×#1658 | semidirect |
| 76. #564 | C2×D71 | semidirect |
| 137. C2 | #22587642 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986365 | 2 |
| #22587642 | 2 |
| C2×#17985741 | 2 |
| C2×#564×C71 | 2 |
| C2×#1658 | 71 |