Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
358 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 111 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. #22590114 | C2 | semidirect |
| 3. #22590112 | C2 | semidirect |
| 6. #22586436 | C2 | semidirect |
| 7. C71×#1382 | C2 | semidirect |
| 12. C2×#14556067 | C4 | semidirect |
| 13. C2×C16×D71 | C4 | semidirect |
| 146. #1382 | D71 | semidirect |
| 147. C71 | #12832 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986415 | 2 |
| #22590114 | 2 |
| #22590112 | 2 |
| #22588387 | 2 |
| #22588383 | 2 |
| #22586436 | 2 |
| C71×#1382 | 2 |
| #12832 | 71 |