Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1734 conjugacy classes of subgroups; only the 915 normal subgroups are shown.
This group has 1734 conjugacy classes of subgroups — too many to draw. Only its 915 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. C4×#14556038 | C2 | semidirect |
| 4. C42×C71⋊C8 | C2 | semidirect |
| 5. C42×C8×C71 | C2 | semidirect |
| 9. C4×#11765848 | C4 | direct (N × H) |
| 25. #14556038 | C2×C4 | semidirect |
| 26. C4×C71⋊C8 | C2×C4 | semidirect |
| 30. C4×C8×C71 | C2×C4 | semidirect |
| 37. #11765848 | C42 | direct (N × H) |
| 45. C42×C71 | M16 | semidirect |
| 58. C8×C71 | C2×C42 | semidirect |
| 59. C71⋊C8 | C2×C42 | semidirect |
| 64. C4×C71 | C4×M16 | semidirect |
| 76. C42×C8 | D71 | semidirect |
| 77. C71 | C42×M16 | semidirect |
| 102. C4×C8 | C4×D71 | semidirect |
| 117. C42 | #11765848 | direct (N × H) |
| 131. C8 | C42×D71 | semidirect |
| 138. C4 | C4×#11765848 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#11765848 | 2 |
| C43×D71 | 2 |
| C4×#14556038 | 2 |
| C42×C71⋊C8 | 2 |
| C42×C8×C71 | 2 |
| C42×M16 | 71 |