Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
240 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 3. Q16×C71⋊C8 | C2 | semidirect |
| 4. #22586403 | C2 | semidirect |
| 5. #22586395 | C2 | semidirect |
| 7. C71×#2225 | C2 | semidirect |
| 61. Q16×C71 | SD16 | semidirect |
| 93. C71⋊C8 | SD32 | semidirect |
| 111. #2225 | D71 | semidirect |
| 118. C71 | #12417 | semidirect |
| 162. Q16 | #11765852 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590380 | 2 |
| #22587933 | 2 |
| Q16×C71⋊C8 | 2 |
| #22586403 | 2 |
| #22586395 | 2 |
| #22586387 | 2 |
| C71×#2225 | 2 |
| #12417 | 71 |