Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
328 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 83 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. #22587129 | C2 | semidirect |
| 2. #22587128 | C2 | semidirect |
| 6. C71⋊#1309 | C2 | semidirect |
| 7. C71×#1574 | C2 | semidirect |
| 148. #1574 | D71 | semidirect |
| 153. C71 | #10612 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22587129 | 2 |
| #22587128 | 2 |
| #22587009 | 2 |
| #22587007 | 2 |
| C71⋊#1309 | 2 |
| C71×#1574 | 2 |
| #10612 | 71 |