Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
696 conjugacy classes of subgroups; only the 255 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 255 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 |
|---|---|---|
| 2. #22589055 | C2 | semidirect |
| 4. #22588894 | C2 | semidirect |
| 6. #22588483 | C2 | semidirect |
| 7. C71×#1842 | C2 | semidirect |
| 29. #14556122 | C8 | semidirect |
| 60. Dic71⋊C4 | C2×C8 | semidirect |
| 75. C42×C71 | C2×C8 | semidirect |
| 124. #1842 | D71 | semidirect |
| 126. C71 | #23375 | semidirect |
| 194. C42 | C8×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14556122 | 2 |
| #22589055 | 2 |
| #22588945 | 2 |
| #22588894 | 2 |
| #22588516 | 2 |
| #22588483 | 2 |
| C71×#1842 | 2 |
| #23375 | 71 |