Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
398 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 95 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. #22590590 | C2 | semidirect |
| 2. #22590589 | C2 | semidirect |
| 3. #22587954 | C2 | semidirect |
| 4. C16×C71⋊C8 | C2 | semidirect |
| 5. C71×#2246 | C2 | semidirect |
| 35. C71⋊C16 | D8 | semidirect |
| 43. C16×C71 | D8 | semidirect |
| 56. C71⋊C8 | D16 | semidirect |
| 72. #2246 | D71 | semidirect |
| 75. C71 | #12515 | semidirect |
| 113. C16 | #11765850 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590590 | 2 |
| #22590589 | 2 |
| #22587954 | 2 |
| C16×C71⋊C8 | 2 |
| C71×#2246 | 2 |
| #12515 | 71 |