Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
562 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 562 conjugacy classes of subgroups — too many to draw. Only its 218 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C4×Q8×C13 ◁ C8×Q8×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C13×#3391 | C2 | semidirect |
| 2. Q8×C13×D8 | C2 | semidirect |
| 3. C13×#2240 | C2 | semidirect |
| 4. C13×#2224 | C2 | semidirect |
| 5. C13×#2206 | C2 | semidirect |
| 6. Q8×C13×C16 | C2 | semidirect |
| 7. C4×C13×D16 | C2 | semidirect |
| 46. #33925 | C13 | direct (N × H) |
| 61. C13×D8 | #41 | semidirect |
| 73. #3391 | C2×C13 | semidirect |
| 74. Q8×D8 | C2×C13 | semidirect |
| 75. #2240 | C2×C13 | semidirect |
| 76. #2224 | C2×C13 | semidirect |
| 77. #2206 | C2×C13 | semidirect |
| 78. Q8×C16 | C2×C13 | semidirect |
| 79. C4×D16 | C2×C13 | semidirect |
| 83. Q8×C13 | D16 | semidirect |
| 170. D8 | C13×#41 | semidirect |
| 182. C13 | #33925 | direct (N × H) |
| 186. Q8 | C13×D16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#3391 | 2 |
| Q8×C13×D8 | 2 |
| C13×#2240 | 2 |
| C13×#2224 | 2 |
| C13×#2206 | 2 |
| Q8×C13×C16 | 2 |
| C4×C13×D16 | 2 |
| #33925 | 13 |