Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
472 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 202 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C67 | C22×D16 |
| commutator, Frattini, cosocle | C16 | C24×C67 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C67 ◁ #41×C67 ◁ #131×C67 ◁ #504×C67 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C67×#3415 | C2 | semidirect |
| 2. C67×#2263 | C2 | semidirect |
| 3. C67×#2262 | C2 | semidirect |
| 4. C2×D32×C67 | C2 | semidirect |
| 5. C67×#2258 | C2 | semidirect |
| 8. #508×C67 | C22 | semidirect |
| 9. C2×D16×C67 | C22 | semidirect |
| 11. Q64×C67 | C22 | semidirect |
| 12. SD64×C67 | C22 | semidirect |
| 13. D32×C67 | C22 | semidirect |
| 14. D32×C67 | C22 | semidirect |
| 15. M64×C67 | C22 | semidirect |
| 16. C2×C32×C67 | C22 | semidirect |
| 60. #33982 | C67 | direct (N × H) |
| 64. #3415 | C2×C67 | semidirect |
| 65. #2263 | C2×C67 | semidirect |
| 66. #2262 | C2×C67 | semidirect |
| 67. C2×D32 | C2×C67 | semidirect |
| 68. #2258 | C2×C67 | semidirect |
| 69. C67 | #33982 | direct (N × H) |
| 72. #508 | C22×C67 | semidirect |
| 73. C2×D16 | C22×C67 | semidirect |
| 75. Q64 | C22×C67 | semidirect |
| 76. SD64 | C22×C67 | semidirect |
| 77. D32 | C22×C67 | semidirect |
| 78. D32 | C22×C67 | semidirect |
| 79. M64 | C22×C67 | semidirect |
| 80. C2×C32 | C22×C67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C67×#3415 | 2 |
| C67×#2263 | 2 |
| C67×#2262 | 2 |
| C2×D32×C67 | 2 |
| C67×#2258 | 2 |
| #33982 | 67 |