Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
256 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 71 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. #22590478 | C2 | semidirect |
| 3. #22587932 | C2 | semidirect |
| 4. C8×D568 | C2 | semidirect |
| 5. #22586394 | C2 | semidirect |
| 6. #22586387 | C2 | semidirect |
| 7. C71×#1367 | C2 | semidirect |
| 57. D568 | SD16 | semidirect |
| 93. C8×C71 | D16 | semidirect |
| 121. #1367 | D71 | semidirect |
| 124. C71 | #12416 | semidirect |
| 211. C8 | D1136 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590478 | 2 |
| #22590376 | 2 |
| #22587932 | 2 |
| C8×D568 | 2 |
| #22586394 | 2 |
| #22586387 | 2 |
| C71×#1367 | 2 |
| #12416 | 71 |