Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
658 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 658 conjugacy classes of subgroups — too many to draw. Only its 103 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. #22599267 | C2 | semidirect |
| 3. #22593293 | C2 | semidirect |
| 4. #22587020 | C2 | semidirect |
| 5. #22586836 | C2 | semidirect |
| 6. #22586242 | C2 | semidirect |
| 7. C71×#1478 | C2 | semidirect |
| 118. C2×D4×C71 | SD16 | semidirect |
| 222. #1478 | D71 | semidirect |
| 224. C71 | #10240 | semidirect |
| 313. C2×D4 | #11765854 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599267 | 2 |
| #22597804 | 2 |
| #22593293 | 2 |
| #22587020 | 2 |
| #22586836 | 2 |
| #22586242 | 2 |
| C71×#1478 | 2 |
| #10240 | 71 |