Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
552 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 1. C2×#11718840 | C2 | semidirect |
| 3. C2×#11718850 | C2 | semidirect |
| 4. C2×#11718110 | C2 | semidirect |
| 5. C2×#11718106 | C2 | semidirect |
| 6. #13112941 | C2 | semidirect |
| 7. C13×#2141 | C2 | semidirect |
| 39. C2×C13×Q16 | D4 | semidirect |
| 75. #88057 | D4 | semidirect |
| 77. #88052 | D4 | semidirect |
| 147. #2141 | D13 | semidirect |
| 249. C2×Q16 | D52 | semidirect |
| 353. C13 | #13317 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11718840 | 2 |
| #13124446 | 2 |
| C2×#11718850 | 2 |
| C2×#11718110 | 2 |
| C2×#11718106 | 2 |
| #13112941 | 2 |
| C13×#2141 | 2 |
| #13317 | 13 |