Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
602 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 602 conjugacy classes of subgroups — too many to draw. Only its 151 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. #22598920 | C2 | semidirect |
| 2. #22598917 | C2 | semidirect |
| 3. #22590613 | C2 | semidirect |
| 4. #22590589 | C2 | semidirect |
| 5. #22590564 | C2 | semidirect |
| 6. #22590425 | C2 | semidirect |
| 7. #22590184 | C2 | semidirect |
| 8. C4×C16×D71 | C2 | semidirect |
| 9. C71×#2240 | C2 | semidirect |
| 102. C71⋊C16 | #41 | semidirect |
| 142. C4×D71 | D16 | semidirect |
| 179. #2240 | D71 | semidirect |
| 183. C71 | #33733 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598920 | 2 |
| #22598917 | 2 |
| #22590613 | 2 |
| #22590589 | 2 |
| #22590564 | 2 |
| #22590425 | 2 |
| #22590184 | 2 |
| C4×C16×D71 | 2 |
| C71×#2240 | 2 |
| #33733 | 71 |