Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
558 conjugacy classes of subgroups; only the 199 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 199 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. #13117118 | C2 | semidirect |
| 3. #13117117 | C2 | semidirect |
| 4. #13117116 | C2 | semidirect |
| 7. C13×#2254 | C2 | semidirect |
| 47. C16×D13 | Q8 | semidirect |
| 71. C13×C16 | C2×Q8 | semidirect |
| 72. #6090 | C2×Q8 | semidirect |
| 77. #2254 | D13 | direct (N × H) |
| 150. D13 | #2254 | direct (N × H) |
| 174. C16 | Q8×D13 | semidirect |
| 175. C13 | C2×#2254 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D13×#500 | 2 |
| #13117118 | 2 |
| #13117117 | 2 |
| #13117116 | 2 |
| D13×#367 | 2 |
| C4×C16×D13 | 2 |
| C13×#2254 | 2 |
| C2×#2254 | 13 |