Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
280 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 91 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. #22590615 | C2 | semidirect |
| 3. #22590568 | C2 | semidirect |
| 5. #22587937 | C2 | semidirect |
| 7. C71×#1311 | C2 | semidirect |
| 68. C16×C71 | SD16 | semidirect |
| 110. #1311 | D71 | semidirect |
| 111. C71 | #12508 | semidirect |
| 172. C16 | #11765854 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590615 | 2 |
| #22590596 | 2 |
| #22590568 | 2 |
| #22590564 | 2 |
| #22587937 | 2 |
| #22587932 | 2 |
| C71×#1311 | 2 |
| #12508 | 71 |