Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
508 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 508 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. #22601329 | C2 | semidirect |
| 3. #22590593 | C2 | semidirect |
| 4. #22590403 | C2 | semidirect |
| 5. #22590386 | C2 | semidirect |
| 6. C4×Dic568 | C2 | semidirect |
| 8. Q8×C16×C71 | C2 | semidirect |
| 122. Q8×C16 | D71 | semidirect |
| 125. C71 | #33960 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22601329 | 2 |
| #22590601 | 2 |
| #22590593 | 2 |
| #22590403 | 2 |
| #22590386 | 2 |
| C4×Dic568 | 2 |
| C4×D1136 | 2 |
| Q8×C16×C71 | 2 |
| #33960 | 71 |