Finite Group DatabasebetaFinite Group DatabasebetaOrder 13184.
216 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 88 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×C103 | C2×C22⋊C4 |
| commutator | C2×C4 | C22×C4×C103 |
| Frattini, cosocle | C42 | C23×C103 |
| prime radical | #121×C103 | C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C103 ◁ C2×C42×C103 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #432×C103 | C2 | semidirect |
| 3. C4×M16×C103 | C2 | semidirect |
| 4. #330×C103 | C2 | semidirect |
| 5. #329×C103 | C2 | semidirect |
| 90. #1529 | C103 | direct (N × H) |
| 91. C103 | #1529 | direct (N × H) |
| 93. #432 | C2×C103 | semidirect |
| 94. C4×M16 | C2×C103 | semidirect |
| 95. #330 | C2×C103 | semidirect |
| 96. #329 | C2×C103 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #529×C103 | 2 |
| #432×C103 | 2 |
| C4×M16×C103 | 2 |
| #330×C103 | 2 |
| #329×C103 | 2 |
| #1529 | 103 |