Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
400 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 184 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×C107 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C107 |
| prime radical | C22×D4×C107 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C107 ◁ C2×C42×C107 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #533×C107 | C2 | semidirect |
| 3. #489×C107 | C2 | semidirect |
| 4. #488×C107 | C2 | semidirect |
| 5. #419×C107 | C2 | semidirect |
| 7. C4×M16×C107 | C2 | semidirect |
| 11. C4⋊Q8×C107 | C22 | semidirect |
| 12. #125×C107 | C22 | semidirect |
| 21. #103×C107 | C22 | semidirect |
| 23. #97×C107 | C22 | semidirect |
| 24. C4×C8×C107 | C22 | semidirect |
| 83. #3140 | C107 | direct (N × H) |
| 84. C107 | #3140 | direct (N × H) |
| 85. #533 | C2×C107 | semidirect |
| 87. #489 | C2×C107 | semidirect |
| 88. #488 | C2×C107 | semidirect |
| 89. #419 | C2×C107 | semidirect |
| 91. C4×M16 | C2×C107 | semidirect |
| 95. C4⋊Q8 | C22×C107 | semidirect |
| 96. #125 | C22×C107 | semidirect |
| 105. #103 | C22×C107 | semidirect |
| 107. #97 | C22×C107 | semidirect |
| 108. C4×C8 | C22×C107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #533×C107 | 2 |
| C2×#124×C107 | 2 |
| #489×C107 | 2 |
| #488×C107 | 2 |
| #419×C107 | 2 |
| #418×C107 | 2 |
| C4×M16×C107 | 2 |
| #3140 | 107 |