Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
552 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 165 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 |
|---|---|---|
| 2. #22590597 | C2 | semidirect |
| 3. #22590382 | C2 | semidirect |
| 4. #22590380 | C2 | semidirect |
| 5. Q8×C71⋊C16 | C2 | semidirect |
| 6. C4×#14556071 | C2 | semidirect |
| 7. C71×#3395 | C2 | semidirect |
| 58. C71⋊C16 | #41 | semidirect |
| 76. Q8×C71 | SD32 | semidirect |
| 107. #3395 | D71 | semidirect |
| 114. C71 | #33959 | semidirect |
| 183. Q8 | #14556071 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22601315 | 2 |
| #22590597 | 2 |
| #22590382 | 2 |
| #22590380 | 2 |
| Q8×C71⋊C16 | 2 |
| C4×#14556071 | 2 |
| C71×#3395 | 2 |
| #33959 | 71 |