Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
304 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 4. #22586398 | C2 | semidirect |
| 5. Q8⋊(C71⋊C16) | C2 | semidirect |
| 6. #22586304 | C2 | semidirect |
| 7. Q8×Q16×C71 | C2 | semidirect |
| 68. Q16×C71 | SD16 | semidirect |
| 90. Q8×C71 | SD32 | semidirect |
| 128. Q8×Q16 | D71 | semidirect |
| 135. C71 | #12354 | semidirect |
| 189. Q16 | #11765852 | semidirect |
| 218. Q8 | #14556071 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590565 | 2 |
| #22590380 | 2 |
| #22587700 | 2 |
| #22586398 | 2 |
| Q8⋊(C71⋊C16) | 2 |
| #22586304 | 2 |
| Q8×Q16×C71 | 2 |
| #12354 | 71 |