Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
372 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 73 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. #22589959 | C2 | semidirect |
| 3. #22588389 | C2 | semidirect |
| 4. #22586334 | C2 | semidirect |
| 5. #22586332 | C2 | semidirect |
| 6. #22586330 | C2 | semidirect |
| 7. C71×#1342 | C2 | semidirect |
| 186. #1342 | D71 | semidirect |
| 189. C71 | #11872 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598004 | 2 |
| #22589959 | 2 |
| #22588389 | 2 |
| #22586334 | 2 |
| #22586332 | 2 |
| #22586330 | 2 |
| C71×#1342 | 2 |
| #11872 | 71 |