Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
930 conjugacy classes of subgroups; only the 250 normal subgroups are shown.
This group has 930 conjugacy classes of subgroups — too many to draw. Only its 250 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C8×C13 | #127 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| socle | C2×C13 | #2397 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C13 ◁ C22×C8×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C13×#2955 | C2 | semidirect |
| 2. C13×#2929 | C2 | semidirect |
| 3. C13×#2098 | C2 | semidirect |
| 4. C13×#2091 | C2 | semidirect |
| 5. C13×#2017 | C2 | semidirect |
| 6. C13×#2010 | C2 | semidirect |
| 7. C13×#1747 | C2 | semidirect |
| 50. C13×#97 | D4 | semidirect |
| 51. C4×C8×C13 | D4 | semidirect |
| 52. #23794 | C13 | direct (N × H) |
| 86. #2955 | C2×C13 | semidirect |
| 87. #2929 | C2×C13 | semidirect |
| 88. #2098 | C2×C13 | semidirect |
| 89. #2091 | C2×C13 | semidirect |
| 90. #2017 | C2×C13 | semidirect |
| 91. #2010 | C2×C13 | semidirect |
| 92. #1747 | C2×C13 | semidirect |
| 169. #97 | D4×C13 | semidirect |
| 170. C4×C8 | D4×C13 | semidirect |
| 208. C13 | #23794 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#2955 | 2 |
| C13×#2929 | 2 |
| C13×#2098 | 2 |
| C13×#2091 | 2 |
| C13×#2017 | 2 |
| C13×#2010 | 2 |
| C13×#1747 | 2 |
| #23794 | 13 |