Finite Group DatabasebetaFinite Group DatabasebetaOrder 13184.
312 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 116 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C103 | C2×D4 |
| commutator | C2×C4 | C22×C4×C103 |
| Frattini, cosocle | C42 | C23×C103 |
| socle | C22×C103 | C2×C22⋊C4 |
| prime radical | C22×D4×C103 | C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C103 ◁ C2×C42×C103 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #431×C103 | C2 | semidirect |
| 3. #423×C103 | C2 | semidirect |
| 4. D4⋊C8×C103 | C2 | semidirect |
| 17. C4⋊C8×C103 | C22 | semidirect |
| 19. C4×C8×C103 | C22 | semidirect |
| 50. D4×C103 | M16 | semidirect |
| 89. #1486 | C103 | direct (N × H) |
| 90. C103 | #1486 | direct (N × H) |
| 92. #431 | C2×C103 | semidirect |
| 93. #423 | C2×C103 | semidirect |
| 94. D4⋊C8 | C2×C103 | semidirect |
| 107. C4⋊C8 | C22×C103 | semidirect |
| 109. C4×C8 | C22×C103 | semidirect |
| 140. D4 | M16×C103 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D4×C103 | 2 |
| #431×C103 | 2 |
| #423×C103 | 2 |
| D4⋊C8×C103 | 2 |
| #1486 | 103 |