Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
536 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 85 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. #22596302 | C2 | semidirect |
| 5. #22586165 | C2 | semidirect |
| 6. #22586165 | C2 | semidirect |
| 7. C71×#1271 | C2 | semidirect |
| 73. C2×Dic142 | SD16 | semidirect |
| 123. C4⋊C4×C71 | SD16 | semidirect |
| 223. #1271 | D71 | semidirect |
| 224. C71 | #7748 | semidirect |
| 339. C4⋊C4 | #11765854 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22596302 | 2 |
| #22589574 | 2 |
| #22589430 | 2 |
| #22586165 | 2 |
| C71×#1271 | 2 |
| #7748 | 71 |