Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
814 conjugacy classes of subgroups; only the 199 normal subgroups are shown.
This group has 814 conjugacy classes of subgroups — too many to draw. Only its 199 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. #22590593 | C2 | semidirect |
| 4. #22590592 | C2 | semidirect |
| 5. #22590591 | C2 | semidirect |
| 7. C71×#2247 | C2 | semidirect |
| 90. C4×D71 | Q32 | semidirect |
| 104. C4×C71 | C2×Q32 | semidirect |
| 109. Dic71 | C2×Q32 | semidirect |
| 113. D71 | #2247 | direct (N × H) |
| 119. #2247 | D71 | direct (N × H) |
| 121. C71 | C2×#2247 | semidirect |
| 221. C4 | Q32×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q32×D71 | 2 |
| #494×D71 | 2 |
| #22590593 | 2 |
| #22590592 | 2 |
| #22590591 | 2 |
| C4×C16×D71 | 2 |
| C71×#2247 | 2 |
| C2×#2247 | 71 |