Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
498 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 112 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. M32×#261 | C2 | semidirect |
| 4. #108×#261 | C2 | semidirect |
| 5. #13129912 | C2 | semidirect |
| 6. #13129911 | C2 | semidirect |
| 22. #11718278 | C4 | semidirect |
| 26. C13×#361 | C4 | semidirect |
| 27. #11718155 | C4 | semidirect |
| 28. #11718108 | C4 | semidirect |
| 29. #11718087 | C4 | semidirect |
| 54. #88103 | C2×C4 | semidirect |
| 63. #88098 | C2×C4 | semidirect |
| 65. C13×M32 | C2×C4 | semidirect |
| 66. C13×#108 | C2×C4 | semidirect |
| 68. #88059 | C2×C4 | semidirect |
| 69. #88052 | C2×C4 | semidirect |
| 185. #361 | #261 | direct (N × H) |
| 205. #261 | #361 | direct (N × H) |
| 234. M32 | C2×#261 | semidirect |
| 241. #108 | C2×#261 | semidirect |
| 308. C13 | C4×#361 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×#261 | 2 |
| D13⋊#361 | 2 |
| M32×#261 | 2 |
| #108×#261 | 2 |
| #13129912 | 2 |
| #13129911 | 2 |
| D13×#361 | 2 |
| C4×#361 | 13 |