Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
340 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22590143 | C2 | semidirect |
| 3. #22586396 | C2 | semidirect |
| 4. #22586385 | C2 | semidirect |
| 5. C71×#1564 | C2 | semidirect |
| 122. #1564 | D71 | semidirect |
| 125. C71 | #11951 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598919 | 2 |
| #22590143 | 2 |
| #22586396 | 2 |
| #22586385 | 2 |
| C71×#1564 | 2 |
| #11951 | 71 |