Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
536 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 101 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×#14556136 | C2 | semidirect |
| 3. #22586791 | C2 | semidirect |
| 4. #22586780 | C2 | semidirect |
| 5. #22586230 | C2 | semidirect |
| 6. #22586178 | C2 | semidirect |
| 7. C71×#1525 | C2 | semidirect |
| 215. #1525 | D71 | semidirect |
| 220. C71 | #9211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598394 | 2 |
| C4×#14556136 | 2 |
| #22586791 | 2 |
| #22586780 | 2 |
| #22586230 | 2 |
| #22586178 | 2 |
| C71×#1525 | 2 |
| #9211 | 71 |