Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
370 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 168 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×C131 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C131 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C131 ◁ #117×C131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #540×C131 | C2 | semidirect |
| 2. #478×C131 | C2 | semidirect |
| 3. #469×C131 | C2 | semidirect |
| 4. #466×C131 | C2 | semidirect |
| 5. #459×C131 | C2 | semidirect |
| 6. #424×C131 | C2 | semidirect |
| 71. C131 | #3259 | direct (N × H) |
| 72. #3259 | C131 | direct (N × H) |
| 73. #540 | C2×C131 | semidirect |
| 74. #478 | C2×C131 | semidirect |
| 75. #469 | C2×C131 | semidirect |
| 76. #466 | C2×C131 | semidirect |
| 77. #459 | C2×C131 | semidirect |
| 78. #424 | C2×C131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #540×C131 | 2 |
| #478×C131 | 2 |
| #469×C131 | 2 |
| #466×C131 | 2 |
| #459×C131 | 2 |
| #424×C131 | 2 |
| #3259 | 131 |