Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
398 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 103 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. #22590589 | C2 | semidirect |
| 2. #22587955 | C2 | semidirect |
| 3. C8×C71⋊C16 | C2 | semidirect |
| 4. C71×#1712 | C2 | semidirect |
| 26. C71⋊C16 | D8 | semidirect |
| 42. C8×C71 | D16 | semidirect |
| 58. #1712 | D71 | semidirect |
| 60. C71 | #12515 | semidirect |
| 98. C8 | #14556069 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590589 | 2 |
| #22587955 | 2 |
| C8×C71⋊C16 | 2 |
| C71×#1712 | 2 |
| #12515 | 71 |