Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
578 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 578 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. #22596977 | C2 | semidirect |
| 3. #22587008 | C2 | semidirect |
| 4. #22586652 | C2 | semidirect |
| 5. #22586200 | C2 | semidirect |
| 6. #22586199 | C2 | semidirect |
| 7. C71×#1545 | C2 | semidirect |
| 49. C4⋊(C71⋊C8) | D4 | semidirect |
| 68. C4⋊C8×C71 | D4 | semidirect |
| 220. #1545 | D71 | semidirect |
| 224. C71 | #9198 | semidirect |
| 278. C4⋊C8 | C22⋊D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22596977 | 2 |
| #22594091 | 2 |
| #22587008 | 2 |
| #22586652 | 2 |
| #22586200 | 2 |
| #22586199 | 2 |
| C71×#1545 | 2 |
| #9198 | 71 |