Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
570 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 570 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 1. #22599470 | C2 | semidirect |
| 2. #22599267 | C2 | semidirect |
| 4. #22589313 | C2 | semidirect |
| 5. #22586901 | C2 | semidirect |
| 6. #22586901 | C2 | semidirect |
| 7. C71×#1281 | C2 | semidirect |
| 123. C2×C8×C71 | SD16 | semidirect |
| 202. #1281 | D71 | semidirect |
| 203. C71 | #10221 | semidirect |
| 306. C2×C8 | #11765854 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599470 | 2 |
| #22599267 | 2 |
| #22598786 | 2 |
| #22589313 | 2 |
| #22586901 | 2 |
| C71×#1281 | 2 |
| #10221 | 71 |