Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
390 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 103 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. C4×#14556060 | C2 | semidirect |
| 3. #22586350 | C2 | semidirect |
| 4. C71×#2163 | C2 | semidirect |
| 6. #17986404 | C4 | semidirect |
| 7. #17986376 | C4 | semidirect |
| 12. C4×D568 | C4 | semidirect |
| 127. #2163 | D71 | semidirect |
| 130. C71 | #11744 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598919 | 2 |
| C4×#14556060 | 2 |
| #22586350 | 2 |
| C71×#2163 | 2 |
| #11744 | 71 |