Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
360 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 92 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. M16×#595 | C2 | semidirect |
| 4. C42×#595 | C2 | semidirect |
| 5. #11763681 | C2 | semidirect |
| 6. #11763680 | C2 | semidirect |
| 9. Q8×#595 | C4 | semidirect |
| 11. D4×#595 | C4 | semidirect |
| 21. #10587550 | C4 | semidirect |
| 22. #10587548 | C4 | semidirect |
| 25. C17×#104 | C4 | semidirect |
| 26. #10587508 | C4 | semidirect |
| 27. #10587496 | C4 | semidirect |
| 28. #10587476 | C4 | semidirect |
| 54. C4×#595 | C2×C4 | semidirect |
| 57. #63243 | C2×C4 | semidirect |
| 59. M16×C17 | C2×C4 | semidirect |
| 60. C42×C17 | C2×C4 | semidirect |
| 62. C4×Dic17 | C2×C4 | semidirect |
| 63. #63223 | C2×C4 | semidirect |
| 75. Q8×C17 | C42 | semidirect |
| 77. D4×C17 | C42 | semidirect |
| 88. D68 | C42 | semidirect |
| 98. Dic34 | C42 | semidirect |
| 113. #595 | #104 | direct (N × H) |
| 153. #104 | #595 | direct (N × H) |
| 156. C17 | C4×#104 | semidirect |
| 176. M16 | C2×#595 | semidirect |
| 193. C42 | C2×#595 | semidirect |
| 198. Q8 | C4×#595 | semidirect |
| 205. D4 | C4×#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×#595 | 2 |
| D17⋊#104 | 2 |
| M16×#595 | 2 |
| C42×#595 | 2 |
| #11763681 | 2 |
| #11763680 | 2 |
| #104×D17 | 2 |
| C4×#104 | 17 |