Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
226 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 3. #22586413 | C2 | semidirect |
| 4. #22586412 | C2 | semidirect |
| 5. C71×#1371 | C2 | semidirect |
| 94. #1371 | D71 | semidirect |
| 95. C71 | #12024 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C16×D71 | 2 |
| #22587102 | 2 |
| #22586413 | 2 |
| #22586412 | 2 |
| C71×#1371 | 2 |
| #12024 | 71 |