Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
3650 conjugacy classes of subgroups; only the 331 normal subgroups are shown.
This group has 3650 conjugacy classes of subgroups — too many to draw. Only its 331 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. C2×#17986144 | C2 | semidirect |
| 2. C2×#17986138 | C2 | semidirect |
| 3. #22594064 | C2 | semidirect |
| 4. #22588280 | C2 | semidirect |
| 5. #22588275 | C2 | semidirect |
| 6. #22588252 | C2 | semidirect |
| 7. C22×2−1+4×C71 | C2 | semidirect |
| 55. C2×#41×C71 | D4 | semidirect |
| 62. C22×Q8×C71 | D4 | semidirect |
| 186. C22×2−1+4 | D71 | semidirect |
| 193. C71 | #32885 | semidirect |
| 223. C2×#41 | C22⋊D71 | semidirect |
| 230. C22×Q8 | C22⋊D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986144 | 2 |
| C2×#17986138 | 2 |
| #22594064 | 2 |
| #22588280 | 2 |
| #22588275 | 2 |
| #22588252 | 2 |
| C22×2−1+4×C71 | 2 |
| #32885 | 71 |