Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1010 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 1010 conjugacy classes of subgroups — too many to draw. Only its 251 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. #22587480 | C2 | direct (N × H) |
| 82. C2×Q8×C71 | Q16 | semidirect |
| 109. Q8×C71 | C2×Q16 | semidirect |
| 142. C2×C71 | #1633 | semidirect |
| 151. C71 | C2×#1633 | semidirect |
| 219. C2×Q8 | #11765855 | semidirect |
| 256. Q8 | C2×#11765855 | semidirect |
| 286. C2 | #22587480 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986378 | 2 |
| C2×#17986294 | 2 |
| #22587480 | 2 |
| C2×#17985748 | 2 |
| C2×Q8⋊(C71⋊C8) | 2 |
| C2×Q82×C71 | 2 |
| C2×#1633 | 71 |