Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
452 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 452 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×#3417 | C2 | semidirect |
| 2. C67×#2264 | C2 | semidirect |
| 3. C67×#2262 | C2 | semidirect |
| 4. C2×Q64×C67 | C2 | semidirect |
| 5. C67×#2258 | C2 | semidirect |
| 59. #33984 | C67 | direct (N × H) |
| 63. #3417 | C2×C67 | semidirect |
| 64. #2264 | C2×C67 | semidirect |
| 65. #2262 | C2×C67 | semidirect |
| 66. C2×Q64 | C2×C67 | semidirect |
| 67. #2258 | C2×C67 | semidirect |
| 68. C67 | #33984 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C67×#3417 | 2 |
| C67×#2264 | 2 |
| C67×#2262 | 2 |
| C2×Q64×C67 | 2 |
| C67×#2258 | 2 |
| #33984 | 67 |